To answer your first question, it might simplify things to recast these statements without the double (or, arguably, triple) negative:
- a. Yes, it is possible to do anything.
- b. Yes, it is possible to do something.
We can take these statements in isolation and reword them to be a bit more clear and succinct. This will clarify what is actually being said:
- Original statement: Nothing can be done.
- a. Yes, anything can be done.
- b. Yes, something can be done.
If your intention is to contradict the original statement, then b. is the logical response. The negation of the original statement — nothing can be done — is not that everything (or anything) can be done, but that something can be done. If you negate the statement "Nothing can be done", it follows that "Something can be done", but not that "Everything can be done". It is still possible that "Some things cannot be done."
Now for your second question. The statement "It is not impossible to steal anything" is grammatically correct, but awkward and unnecessarily obfuscated by the double negative. Your suggestion of
Anything can be stolen.
gets at the meaning correctly and is much more clear.