Absolutely, yes, insofar as they can refuse to include a transaction in a block (hat tip @bass)

Try submitting a zero-fee transaction. You'll probably find it gets censored by many miners :-)

However there are also many miners who would include it, in order to claim the tx fee. It is assumed that miners are motivated by profit-maximisation.

In the end, the miner (or pool) with the most proof of work can choose the transactions to include, which could include zero transactions, eg in the case of an attack.