Are Fingerprints Removeable?

Are fingerprints removable? Yes.

Are fingerprints removable without damaging the coin or hurting it's value? Ah, that's the tricky thing. Short answer: no, not unless you really know what you're doing.

Fingerprints on copper are basically permanent. If you touch a red copper coin with your fingers, give the coin a wash in acetone straight away. If you let the fingerprint oils react with the copper, the prints can only be removed with acids or other harsh treatment. NCS and other coin conservators use very tightly focussed (and highly secret) treatments to remove prints without damaging the surrounding metal, with great care and at great cost - they charge a minimum of $20, more for expensive items.

Fingerprints on silver are less noticeable, unless it's a proof coin. Again, washing the oils off the coin with acetone is better than trying to remove a fully developed print.

Sort of as noted but not completly. For almost any coin if it has a finger print on it and it was made really recently, might just come right off with Acetone. The longer one stays on a coin, the more the chances are they will not come off. Also, fingerprintss on coins are pending the individual's body chemistry. Some people have extensively high acidic sweat and others have very little acid. The higher the acid content of their sweat, the more damaging the fingerprint. Also, the oils a person's body emits has different properites that may or may not have effects on metals. When you consider the numerous different contents of a person's sweat, moisture, oils and acids, some fingerprints come off easily and some are there forever. Also, the amount of time they are on a coin makes a similar difference.
I purchased a 1995 Lincoln Cent Double Die for a few dollars since it had a massive thumb print on the front. One dip in Acetone did very little to remove it but some Jewlery cleaner from Walmart completely removed that print. Since that coin was about MS-65, no one could ever tell anything except it looks new which is basically was.
Of course on older coins and dirty coins, that Jewlery cleaner would really be noticed.