It seems to me that there is a difference between an unprovable sentence, and an undecidable sentence, but sometimes I have the impression that some authors use the terms interchangeably.
In my understanding, if something is undecidable, then it is obviously unprovable, because if we could prove it, then we would have decided that it is true. But there may be some sentences (due to Gödel, if I'm not mistaken?) which cannot be proved but yet are either "true" or "false".
Now, do phrases like "In my opinion [unprovable sentence here] is true" make sense? What if it was about an undecidable sentence? If I'm not mistaken again, undecidable sentences can be added as axioms to our system (for example, the axiom of choice is undecidable in ZF). But what about unprovable sentences that are not undecidable? Can they also be added as axioms? Would it lead to an inconsistency if the sentence is "false"? I don't even know what false means here.
Important EDIT: I wrote the whole question without realising that some questions are trivially unprovable. What I meant by "unprovable sentence" was "a sentence which is unprovable, and also its negation is unprovable".
One thing that came to my mind now: when one says that "if $P$ is false, then $P$ is unprovable", it seems to me that he is assuming that the current system of axioms is consistent. It also seems that, in everyday-mathematics, it is normal to assume that the system is consistent. Does it mean that it's not harmful to write "if $P$ is false, then $P$ is unprovable" ?