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.