Removing Adhesive And Paper From Old Copper Coins

Xylene is what I'd try first, then Acetone, either should blast it off and not affect the coin in a detrimental way.

Sunlight in an older brown envelope (like on a window sill) just not a UV blocking window might get them to turn a bit darker over a few months time.
Deller's darkener might also help somewhat, I would never suggest using it unless the coins have little value or you just want to experiment on them. It is a petroleum based sulfur powder mix (I think) that darkens copper with a little application. I have tried it myself with somewhat satisfactory results. Never on coins I was reselling - or not at least without disclosing the color had been altered. It did leave a slight oily sheen on them and they smelled like vas aline afterwards, a tell tale sign that it's been used for sure.

I'm guessing these coins were glued onto a board with paper that had written description about them printed on it. I've seen stuff like this back in the 1970's it was quite popular with rock and mineral collections also, stuff you might find at a tourist spot for sale.

Looks like it. Acetone should not hurt the coin, (use pure acetone, not the nail polish remover it likely has other junk in it. Acetone is available at most hardware stores in quart cans for under $5.00 or there about. Xylene I don't use often enough to know how it works, but I've never had acetone do anything other than remove gunk like you mention, never had a coin change color, other than as you remove stuff from the surface, the color underneath may have caused the coin to tone differently, acetone is pretty safe on metals, just don't breath it or use it in a plastic dish. I have a small ceramic bowl I keep for coin restoration with acetone, I do it out side to keep the fumes out of my lungs. I also use cotton q-tips to help with some of the more stubborn gunk, only on already circulated coins of course. A longer soaking may be desired, if so use a glass jar with a lid - as acetone will evaporate fairly quickly, I've left coins in for several days with no ill effects., I do change out the acetone as it gets dirty, and never reuse it. I dispose of it by pouring it in a hole in the corner of my yard, then cover it with a handful of dirt the next day, most of it will evaporate, Absolutely no smoking or any flames near it or the can, it is highly flammable.

Same as water, don't worry, you won't hurt the coins! No need to dry afterwards it will evaporate by itself.

Good point, depending on where you live the water may have a lot of minerals in it, distilled water is best to use, as it is quite neutral as to ph and acidity.
I almost always use acetone and can't remember the last time I used water at all, must have been more than 10 years ago, I've never had any issue with acetone on my coins.

The only time I'm not happy is when a contaminate (gunk) comes off and the color is different due to toning or patina difference from the offending matter, which is now removed so there is usually a much lighter spot. But I recon it is better to remove any organic material that may continue to etch into the coins' surface over time causing pitting or more corrosion.