1. How are those set and where? Is the fee set on each transaction? Can I choose to pay as much as I want?
The sender of the transaction sets the fee for that transaction, and it can be as much or as little as they choose. Note that competently designed wallet software will automatically choose an appropriate fee based on current conditions; it is not normally necessary to choose a fee manually.
2. Is it percentage or fixed?
It is proportional to the number of bytes of data the transaction requires, since that's the limiting factor in including transactions in a block.
3. The miner of the latest block gets all the fees for the transaction in that block? Or is it more complicated?
Yes, it's that simple.