I see all kinds of transaction confirmation times on Blockchain.info, from really short to very long (to an unacceptable extent). I wonder if there's a way to control that in any way. Maybe by giving a bigger reward to the miners? Does the sender even have control over this? I know that Ethereum has some control over that, but is it possible for Bitcoin? What about other crypto coins/tokens?
A bigger amount to the miners won't make them mine the block faster. It will only increase your chances to be in the next block AKA have your transaction confirmed faster.
In short the answer is no, the sender has no control when the next block will be mined, nor can they influence that with higher fees on their transaction.
"Miners" try to solve a mathematic problem using their collective computing power / hashrate.
A higher amount of fees doesn't drive the hashpower up, so it seems logic that the speed of "finding" a new hash / creating a new block doesn't increase.