Is it technically possible to change the total amount of Bitcoin? Also, is it possible to change the reward cycle duration or the number of mining- reward coins?
Technically, yes, yes, and yes.  However, I'm not sure if we'd still call it "Bitcoin" at that point.

Any of these changes would require a hard fork, which means that the underlying rules of the system are changing in a non-backwards-compatible way.  It means that blocks/transactions from after the fork are not guaranteed to be considered valid to nodes running software for pre-fork.

So, to change Bitcoin like this in practice would require convincing the entire rest of the world to agree with the changes.  Anything less, and you will end up with two versions: the original and the one with your changes.  Which one gets the title "Bitcoin"?  I don't know.  That's a non-technical question, and a point of contention.

For an example of this in practice, see Bitcoin Cash.