Did the FIBRE protocol reduce the occurrence of chain forks? I've just learned that Fibre protocol is used for really fast block propagation. My understanding is that if blocks are propagated faster, miners can more quickly continue to work on (what seems to them) the head of the chain, there is a lower chance for temporary forks to happen and even if they occur, they are likely to be short (small length). Please correct me if I got that wrong. That leads me to two questions:

Is the Fibre protocol the reason for rare temporary forking?
Is the Fibre protocol also the reason why mining difficulty is pretty much the same across the network (I assume it's the same, otherwise it would be problematic, right)? If difficulty changes after 2016 blocks on average and block propagation is fast, everyone can adjust their mining difficulty pretty easy and there wont be much difference inside the network (most of the nodes will up to date)?
Is Fibre protocol deserved for rare temporary forking? If blocks are propagate that fast, there are less chances for temporary fork to happen and even if it do, they are short (small length)? Miner can fast continue to work on (what it seems to him) block head of the chain?

Well the point is that a miner can more quickly switch to a new block that has been found on the network. The time a miner spends on building on top of block A, while a block B has already been found by someone else, is very likely a waste of money and energy.
Note that this is not just in the interest of the miner, but of the entire network: a hypothetical 51% attacker is not subject to these losses, as they only build on top of their own blocks. Thus, faster propagation of blocks on the network means that this advantage 51% attackers have over honest miners is reduced.

Is Fibre protocol deserved why mining difficulty is pretty much the same across the network (I assume it's the same, otherwise it would be problematic, right)? If difficulty changes after 2016 blocks on average and block propagation is fast, everyone can adjust their mining difficulty pretty easy and there wont be much difference inside the network (most of the nodes will up to date)?

No, difficulty is not a function of time, but of the previous blocks. So regardless of which block a miner is working on, they always know exactly what the difficulty of that block needs to be (as they have the block's ancestors).
Better block propagation means they can switch to the next block faster, along with the difficulty change that that entails, however.
PS: Note that as of September 2020 the public FIBRE network is no longer operational, and I don't know if any private deployments exist.