DISCLAIMER: I am not a doctor, anything written here should not be taken as medical advice
To complete Randolf's answer, I will answer part 2 of your question
Do any of those ingredients have known pharmaceutical properties that might help my sinus problems?
Allium Cepa is onion: onions are traditionally used against sore throat, although I could not find any peer-reviewed study on their efficacy. They also contain antioxidants such as quercitin and there are several studies (not sure how conclusive, I have not read them) that show that eating onion and garlic could reduce the risk of cancer.
For your specific case: onion has also antibacteric properties.
Two papers on that:
Anti-bacterial action of onion (Allium cepa L.) extracts against oral pathogenic bacteria.
Antibacterial and antioxidant activities of quercetin oxidation products from yellow onion (Allium cepa) skin.
So, how much quercitine is there in a 6X HPUS solution (that means the original solution is diluted 1000000 times)? I'll do some rough calculation, but bare in mind that this is very approximative and could be off by a few orders of magnitude! Also, I will not repeat this calculation for all the other components, I'll leave it to you :)
- The quercitin content in yellow onions is ~30-300mg/kg (see Quercetin content in yellow onion (Allium cepa L.)), so let's set for an average of 100 mg/kg.
- Now I don't have a clue how they extract the onion, but let's say 10% of it is lost during processing (may be more, may be less, I don't know), if we extract one 100g onion into 1l water we'll end up with ~9mg quercitine. (This is the critical passage. I am assuming 1 100g onion in 1l of water. Anything else and the numbers will vary a lot. Anybody knows what a "standard onion solution" is?)
- The molecular weight of quercitine is 302.24 g/mol, so 9mg/l corresponds to 29.8μM (μM = micromolar, that is 10-6 moles in a liter), which is in the normal range of action of many drugs.
- We dilute that 1 million times and get to a 0.0000298μM solution, that is a 29.8yM (yM is called yoctomolar and corresponds to 10-24 moles in a liter). A mole is defined as the amount of matter containing one number of Avogadro (NA = 6.0221418×1023) of molecules. So 29.8 yM contain approximately 18 molecules of quercitine per liter. Assuming you take a few drops of it, let's say 2ml, you will get approximately 0.04 molecules of it.
Natrum Muraticum is table salt. Already the fact of giving it a some sort of pig-latin name sounds very fishy. It's sodium chloride, NaCl, no need to call it salis magicus or whatever. The solubility of NaCl in water is 359g/l. Supposing they start from a saturated solution, and dilute it 1 million times they'll get 359μg/l. When you cook pasta you put ~10g/l of salt in the water. 1 hot dog contains 1.3 mg of salt. I do not feel the need to go into further details on this.
Histaminum Hydrochloricum (or histamine dihydrochloride, which is its proper chemical name) is marketed as an "unapproved homeopathic" product against cold.
From the Wikipedia page for Zicam, one formulation of Histaminum Hydrochloricum
The only possibly biologically active ingredients present in Zicam Cold Remedy are slightly diluted zinc acetate (2X = 1/100 dilution) and zinc gluconate (1X = 1/10 dilution); the product's other originally active ingredients have been serially diluted to the point that Zicam should no longer contain any molecules of those ingredients, and are listed as "inactive ingredients" on the label.
Histamine dihydrochloride is a salt of histamine, a physiologically occurring compound that is involved in the triggering of inflammation (ever heard of anti-histaminic treatment for allergy? They counteract the effects of histamin). I cannot think of why it would have any positive effect on sinusitis, being a bronchoconstrictor, nor could I find literature at that regard.
As you noted, at biologically active concentrations, histamine dihydrochloride is used as a leukemia treatment.
Luffa Operculata or sponge cucumber is another "unapproved homeopathic" product.
In Brazil it is used as a folk remedy (known as Buchinha), although they don't use it at 12X (remember that in certain cases phytotherapy is not equal to homeopathy, although there is much confusion about it).
At the doses used in traditional Brazilian medicine there is some evidence of toxic effects on the palate for it. At 12X I doubt you'd even had that.
Luffa operculata effects on the epithelium of frog palate: histological features
I found this paper on a rather obscure journal which claims that Luffa Operculata is efficacious against sinusitis.
Efficacy and safety of a fixed-combination homeopathic therapy for sinusitis
Even just by reading the abstract, however, you can conclude that the article is seriously flawed. I do not have access to the full text, unfortunately, but I found this blog post which analyses the article quite well (I love the part where they show that the authors cite papers that show that homeopathy is not efficacious!).
Blinded by pseudo-science?
Galphimia Glauca or thryallis is a plant with nice yellow flowers, yet another FDA-unapproved homeopatic.
One study caught my attention
A homoeopathic proving of Galphimia glauca
If you're not familiar with homeopathy, you should know that the idea is that if substance X causes headache you can dilute it a lot, whilst you do some magic dance, and it will cure headache. This is called a proving.
From the abstract:
Our results confirm the toxicological and clinical effects of Galphimia glauca compared to placebo, but the ICCH criteria for proving symptoms were not suitable to distinguish between specific and unspecific symptoms.
So, essentially, even at doses that do have pharmacological effects, its effects cannot be distinguished from placebo... well, not very impressive, is it?
And, last but not least Nux Vomica, or the strychnine tree. The seeds and bark of this tree contain two potent alkaloids called strychnine and brucine, along with other poisonous substances. In the past strychnine was used for gastrointestinal problems, but has since been abandoned from medical practice.
I could not find any proper medical trials for this.
So, in conclusion, don't waste money on it.