Nothing is impossible, but Bitcoin is open source.  With the size that Bitcoin is now, that means that thousands of the best programmers in the world have failed to find any bugs (well, that the bugs which have been found have been fixed).  Bitcoin is about the closest system to 100% secure in the world - there was a fatal bug very close to the beginning I think, but it was fixed by a hard fork.

So basically, nothing is impossible but I'd say it's pretty damn close.

Everything is possible when someone has the ability to concentrate in a full fledged manner. In a decade everything that looks like a advancement right now will look like nothing. So when the requirement increases the complications increase but solution too will accompany it.

That really depends on the severity of the bug, if users balances get affected, you can be damn sure it'll drop close to 0 dollars.
And you'd be a fool to buy more Bitcoin at that point because it's cheap.

This. Is there is a bug, it should have been found by now. We have been using bitcoin ever since its inception and its not been crippled, of course except for the network spam. So my answer is that for now bitcoin technology is foul proof, unless someone has come up and says they found a glitch on the code.