Sorry, but the vast majority of what you said is shite.
Methyl salicylate is poisonous in large enough quantities. As is basically any chemical on the planet. The question is how much, and how large is likely exposure. In a bottle of mouthwash, the max mass of the chemical per litre is about 0.7 grams, which makes sense given that is the max solubility in water of the material, and then if you wash the bottle out a few times you are going to be diluting that down by a further factor of 1000 at least (extremely conservative, but lets roll with it), so you are looking at a few micrograms of material per litre of final product. Given a human of approximately 50 kg, the recieved dose from a litre of alcohol would be around a factor of 10 million less than the LD50 of an adult human at 0.05g/kg (the most consevative value I could find), and this goes down with every rinse. The flavour threshold, conversely is somewhere around a few to a couple of tens of parts per million, which would still be detectable around this dilution. Hence why it is a good flavouring: it is detectable and flavoursome at quanities far below the toxic limit.
As for the glue, hot glue is primarily formed from a polymer called Ethylene vinyl acetate, which is extremely low toxicity thermoplastic which melts at releatively low temperatures, along with a tackifier resin and parrafin wax. You do not need to burn it for it to become usable, heated to around 60 degrees is sufficient, whereas its decomposition temperature is several hundred and oxidation occurs even higher than that. While it might be possible for traces of the material to permeate into the alcohol, if toxicity via that route were a concern then the material would not be used in multiple situtations where ingestion exposure is likely. EVA is used in mouth guards and as an orally compatible plastic for medical resarch (so basically safe to be in your mouth for some period), Paraffin wax has an LD50 of several kilos per kg, and is used in, among other things, crayons, and in small quantities as a food additive, and tackifier resins are similarly non toxic in likely oral doses. So in other words, problems arsing from infrequent exposure are basically null. I wouldn't reccomend eating it regularly, but a small swallowed amount would do basically nothing.
TLDR: The alchohol you are drinking will do far more damage to your health than the bottle you are drinking it out of.
Source: PhD in Physics, worked with a large amount of nasty chemicals in the last few years studying their electron spectra. Has spent many hours studying MSDS.