Quite simply, no. The claim in the video series you linked is patently ridiculous.1
What is being claimed?
The argument presented in your videos is based entirely on the following passage in the Old Testament book of Song of Solomon.
Song of Solomon 5:16 (ASV)2
16 His mouth is most sweet; Yea, he is altogether lovely. This is my beloved, and this is my friend, O daughters of Jerusalem.
I have highlighted the phrase in question here. The claim in the video is that the phrase translated here as altogether lovely is actually the proper name "Mohammed" with a respectful plural ending and is incorrectly translated to its meaning. The video (and several other sites on the net) suggest taking the root Hebrew word מחמד into an online translator. The results they show have two machine translation sites returning "Mohamed" as the result.3
Why doesn't this mean anything?
The flaw in this argument is that it proves absolutely nothing. To show why, I will give some translation examples from a language I know well. While it is relatively rare in English with our mish-mash of nationalities, in many languages even today (and even more so through history) it is common for proper names to be based words with straight forward meanings in their native tongues. I have Turkish friends with names like Güven, Gül, Nehir and Pınar. In the previous sentences I capitalized them and from the context it is clear that those words refer to people, but these are the ordinary everyday words for trust, rose, river and spring respectively. In fact most of the people I know have names with similar ordinary meanings.
If I were to say "Güven çiçekçiden bir gül aldı," (Güven bought a rose from the florist) there is absolutely no question from the context that I am using Güven as a proper name and gül as a type of flower. You don't even need the capitalization or know my friends names. The immediate context of the words makes it clear how they are being used.
Back to your videos. The accusation is raised that "we have no right to translate names". This is, in itself, true. You will note that in the English translation I provided for the Turkish sentence above, I have done the work of interpreting it for you and retained the proper names but translated the words with ordinary meanings. If I had given the translation as "Trust bought a Gül from the florist", my competence with the language must be called into question. The issue before us is when to translate a word as a name and when to give the meaning. For this, we need the context and to understand the thing we're translating in the first place.
What does the context tell us?
Song of Solomon is a notoriously difficult book to translate. The Hebrew is difficult and sometimes obscure. Even when you sort out the words, it is difficult to interpret what it is all supposed to mean. Jews and Christians differ widely on what to do with the passage, and even among Christian traditions there is some debate as to what the imagery refers to.
However, those interpretation difficulties do not concern us here. Whether or not the passage was intended as an allegory or a plain description, it is clear that the immediate context of the passage is a woman addressing her lover. Even with two different religions claiming this as a holy text and vast differences in interpretation, the simple translation of these particular words has never really been in doubt because the face value translation of מחמד to mean lovely fits the context of both the sentence and the book.
The verses leading up to this are in the voice of the woman describing the physical characteristics of her man. His hair, his eyes, his legs, etc. are all described in terms of appeal and desire. Verse 16 starts out talking about how sweet his mouth is and then says that he is desirable as a whole. Given the context and the time it was written, there is not a shred of evidence this should be translated any other way than it has been in every one of hundreds of languages by thousands of translators.
And the Hebrew?
One of the basic claims in the video is that the -im suffix used on the Hebrew root word should be seen as a respectful plural just as it is in Arabic, where saying "Mohammed-im" does apparently4 have that effect.
According to Gesenius (the standard Hebrew Grammar), the respectful plural is quite foreign to Hebrew. The "let us" passages of Genesis, which many take as plural of majesty, Gesenius takes as self deliberation.
In the verse above, the word מַחְמַד is correctly being translated 'lovely' and the suffix that makes the contextual form of מַחֲמַדִּים is a plural that intensifies the meaning, rendering the final translation 'altogether lovely'. This is not out of place. In fact the entire poem has similar constructs, including the previous line of the same verse. 'Very sweet' is one word, ממתקים, the root ממתק means 'sweet' and the plural makes it 'exceedingly sweet' or 'very sweet'.5 It is utterly irresponsible to take this standard grammar form that translates consistently as an intensifier on a series of adjective and render the final instance as a proper name just because it sounds like one in a later language and translate the suffix as a respectful plural according to the later language rather than the one in which it was written.
But why does it sound the same?
Lots of words in one language might be combined as a series of sounds and understood as something entirely different in another language. The videos include the sound of a Jewish Rabbi reading Hebrew text in question. To an ear that does not speak Hebrew, the combination of sounds making up the name Mohammed are clearly in there.
Linguistically, this is just as absurd as the other line of reasoning. Just because a combination of sounds appearing in the normal course of a language sounds like something else in another language doesn't make it so. If I asked somebody on the street in Turkey "Where can I find a peach?" (in English), they might look at me strange because they only word they heard in their own language was "bastard".
Just because what used to be a root word in one language ends up sounding like a proper name in a later language does not mean that every instance of the original root word is a reference to a famous figure with the later name. The connection simply doesn't mean anything.
And Jesus?
Your question includes a one liner concerning a claim not actually found in your video:
Does Jesus predict the coming of Muhammad in the Bible?
The simple answer to this is no. It is difficult to debunk this "claim" since you haven't even established in the question what the claim is, but let me do your homework for you. The Islamic Research Foundation makes the following claim which you will hear echoed throughout the Muslim world in various forms:
"Ahmed" or "Muhammad" meaning "the one who praises" or "the praised one" is almost the translation of the Greek word Periclytos. In the Gospel of John 14:16, 15:26, and 16:7. The word 'Comforter' is used in the English translation for the Greek word Paracletos which means advocate or a kind friend rather than a comforter. Paracletos is the warped reading for Periclytos. Jesus (pbuh) actually prophesised Ahmed by name. Even the Greek word Paraclete refers to the Prophet (pbuh) who is a mercy for all creatures.
As far as I know, this is the only place the NT or Jesus is commonly claimed to mention Mohamed. I presume is is the subject of your inquiry.
This claim, like the one above, is also patently ridiculous. There are several other variants of this, but they all hinge on really poor linguistics. Determining the meaning of the Greek word παράκλητος in context is not easy. Greek scholar Raymond Brown is often cited by Muslim apologists on this issue because his translation of John keeps a transliteration of the Greek as a sort of name instead of translating the meaning (as most other English translations have done) and rendering it as helper, advocate, comforter or counselor. However, his intention was to clear up the usage and understand it better in context. His understanding of who/what fills the role referred to can be clearly seen from this quote:
Thus the basic function of the Paraclete are twofold: he comes to the disciples and dwells within them, guiding and teaching them about Jesus; but he is hostile to the world and puts the world on trial.
Whether Christian or secular, Greek scholars investigating this passage all conclude that this passage must be understood in context with the related passages from the same authors and time period that describe the coming of the Holy Spirit. Whether you believe in such a thing at all, it is clear that the disciples did based on Jesus words, and that Jesus words as recorded in Greek fit with their contemporary understanding.
Only a series of linguistic flying-leaps can connect this usage with another word in another language that doesn't sound the same but happens to have a similar meaning. Here is a similar series of connections:
My name is derived from a Hebrew name having a connotation of "faithful". The Turkish for faithful is "sadık" which sounds a lot like "sağdıç" meaning groomsmen. Ergo my parents predicted that their son would be somebody's faithful best man.
There are just too many unsupported jumps for this claim to hold water. Even the text from the IRF is worded with tentative phases such as "almost the translation of". They are making the jump from two words in two unrelated languages that have similar meanings to one being a prophecy of the other -- in spite of other solid contextual evidence about the intended meaning being to the contrary.
Footnotes
Frankly this particular claim is one of the weaker ones made. There are several other verses more commonly cited as "proof" that hold more water than this one. There is an Isaiah verse with a similar translation issue. The case holds "more" water because at least it happens to be a prophecy, but still sinks because of the translation issue explained above.
The usage of the ASV translation here was selected at random, the English translation used makes absolutely no difference to the argument. No serious translation work has translated this passage in any other way.
While legitimate as far as it goes, I think it's somewhat telling that given the same input Google translator returns a clue in the form of the noun roots loveliness, delight, desire or charm.
I didn't research the Arabic here, I'm only going off of the popular claim.
Thanks to Frank Luke for some help with the Hebrew grammar here.
