My dog likes to sniff and lick everything that come within its reach, including stray dogs' poops. Is it convenient to keep the muzzle on him for the whole time when we're playing out in the park?

As long as he is properly conditioned to his muzzle and it is a correct fit, with good airflow, then certainly! If we're hiking somewhere and there's even an inkling that we may run into other dogs, I keep mine muzzled (on walks, too).
If a little dog starts a fight, my GSDs will finish it, and all the fingers will point at the big dog. So, I keep them muzzled for liability-sake. It's definitely doable for you.

Depends on what you're wearing a muzzle for your dog. If there is an aggression or biting problem, I think it is best to solve the problem first.