Sure you can. You could figure out the answer yourself without starting another thread to do it for you too. Just go to the Mint's web site and see what individual proof coins are currently listed for sale. US Mint catalog
Regardless of the ambiguity of the OPs question, they could still answer it without this thread by simply reading the offerings on the Mint's web site.
Unless its a single coin offering such as an Eagle or Commemorative, No. The US Mint has not sold individual proof coins of circulation coinage since 1954.
Possibly but I think the likely scenario is that they crack them out of proof sets for various reasons.
The answers to most questions asked on here could be found elsewhere. If you don't like the question, just ignore the thread!
Proof sets get damaged all the time and people also break them up on purpose and sell the ones they don't want to keep.
Yup. You will notice the halves and cents are the most expensive. That is because they have the greatest number of collectors wanting to update their sets. Used to be you could buy nickel and dime proofs for just a little over face. I have a few rolls of proof dimes from the 60's to the 80's actually at home. A dealer offered them to me for about $.25 each one time to clear stock. If a proof set is worth $10 for a 5 coin set, then a dealer will break up the set if he knows he can sell the cent and half for about $10, and the rest will be profit.