Your lips do important work in making a trumpet play. Dolphins don't have the fine control over their lips that would be necessary. Maybe the blowhole does?
A dolphin would likely play something more like a trombone with an articulating system of pipes that could be played through vigorous contortions of the body. Think playing a trombone but with a hula hooping/swimming motion. Perhaps a small lever could extend out to the dolphin flipper that would allow nuanced fine pitch control with lateral contortions of the dolphin’s flipper.
Unlike most of these sorts of things, this one has a definite answer: 2. They cannot blow air out of their mouths. However, since they have no hands to work the valves, it wouldn't sound too good, assuming they could get it to stay in place to begin with.
Valves aren't needed to "sound too good", they're needed to get more notes. Without valves, you've still got the harmonic series. Any piece played on bugle could also be played on trumpet. And the majority of classical compositions up until the late 19th century. (All classical compositions until the early 19th century.)
Probably not. I'm not a brass player or a marine biologist but as I understand it the way a brass player's embouchure works would not be replicable by a dolphin's blowhole (it's not just "send air through the tube", it's more like blowing a raspberry). They wouldn't be able to play any note, let alone different notes.
