The episode in question that OP saw is available on YouTube.
Story 1 : Newlyweds on Honeymoon
Unless details of the story have been extremely modified, this story is false.
Upon watching the story, several inconsistencies arrive.
The couple are identified as an Eric and Mrs. Farley. According to this source there was no one who boarded the Titanic under the surname Farley, nor anyone under either Eric or Erik with a last name resembling Farley phonetically.
The husband states that they are right next to a Mr. John Jacob Astor, Boat Deck, 111-B. Several things wrong here.
The Boat Deck had no accommodations for passengers
B Deck did not go to room 111.
C Deck, where room 111 actually would have been for First Class Passengers, was occupied by a Mr. Benjamin Laventall Foreman, who was traveling alone
Mr. Astor was staying in rooms C-62 and C-64, far away from C-111.
Story 2 : The Minister
The story lists a Dr. Morgan as the Minister of the Rosedale Methodist Church in Winnipeg, Canada during the time of the Titanic sinking. There was indeed a Charles Morgan who was the Cleric of the Rosedale Methodist Church in Winnipeg in 1912.
While there are places online that claim this story to be true, no trustworthy sources seem to be available. None cite their sources, and most of the stories seem to be copy/pasted from each other. The only place where I was able to find anything to be sourced was on Atlantis Rising Magazine which claims that the Toronto Sun was the originator.
A google search points to the Lowell Sun actually being the source, although from the (admittedly terrible) OCR job on the page available as a free sample, it seems to be the same version of the story seen on other pages available online. The article was written in 1975, decades after this episode came out.
Story 3 : The Cartoonist
The man in the story is named as Harry Teller. A google search for "Harry Teller" Titanic only brings up references to the episode in question. A google search for "Harry Teller" cartoonist bring up no relevant results outside of references to the episode.
Similarly, the supposed painting predicting the sinking is shown in the episode. While it's entirely possible that the painting was destroyed, there are no news references to a painting made prior to the Titanic sinking. This story seems to be wholly invented for the purposes of this episode.
Story 4 : The Wreck of the Titan: Or, Futility
TIME Magazine wrote an article about the similarities between the book and the actual disaster. While there are some eerie similarities between the two stories, it seems to be more a case of Pareidolia than anything else.
Notable excerpts from the TIME article:
“He was someone who wrote about maritime affairs,” (Paul) Heyer said. “He was an experienced seaman, and he saw ships as getting very large and the possible danger that one of these behemoths would hit an iceberg.”
The story’s main focus is a Titan naval officer who finds God, gets the love of his life back and fights alcoholism after the Titan’s sinking. Robertson also throws in some interesting action sequences — like one where the protagonist slays a polar bear to rescue a small child.
After the sinking of the Titanic, Robertson gained great acclaim for being a clairvoyant, a title he denied.
“No,” he would reply. “I know what I’m writing about, that’s all.”
Furthermore, the Titanic was not the first, nor would it be the last, ship to sink due to icebergs. Wikipedia provides a non-exhaustive list of ships that have confirmed to have been sank with icebergs. A web archive of icedata.ca provides a larger list of confirmed and suspected sinkings due to icebergs.
Nor would it even be the only ship to sink due to icebergs with a name similar to "Titan". The same source listed a Titania (note the slightly different spelling from Titanic) sinking due to an iceberg in 1880.
So, in conclusion, you have
- A story directly contradicted by freely available evidence
- A story whose only verified claim is that they get the name of a church minister correct
- A story with no available evidence of it being true
- A book that, while bearing similarities to the sinking, uses a highly dangerous and well known sea hazard to sink a ship using a naming convention that was popular at the time