Is it possible to rewrite past transactions in Bitcoin?
Yes. That is one of the reasons it is recommend to wait for more than one confirmation before accepting a bitcoin transaction.
For example, lets say, we have a super computer with any desirable speed, that would be able to calculate hash as fast as we want. Would it be possible to take for such computer, a block that is 2 weeks old from now and create (from that block) a new chain that is bigger than today's chain with its own transactions?
No, since such a computer is itself impossible.
If so, the current network would accept our new (forged) chain and all the past transactions would become invalid.
The question is, as I said, based on an impossible premise. Here are some further obstacles:
1) You can't just invent an arbitrary amount of computing power. There is only so much physical space accessible to mankind. There is only so much energy available.
2) A supercomputer is entirely the wrong tool since supercomputers are general purpose devices. They're absolutely atrocious at attempting to rewrite bitcoin transactions. Honest miners with specialized equipment would have a huge advantage.
3) So say instead of a supercomputer, you spent a billion dollars to build a device specifically to do this. You would be able to do this exactly once. The community would react by either changing the mining algorithm or other means that produce the same effect. So you would get this one attack and then you would have a billion dollar paperweight.
4) Even if you thought that was all worth it to shake confidence in bitcoin, it would likely backfire. What would happen is that bitcoin will have recovered from your billion dollar attack, you'd be out a billion dollars, and bitcoin would still keep going.