Shooting underwater: The few times I've seen it tested with a semi-auto pistol, it fires fine, once, then the density and drag of the water prevents the slide from cycling reliably, and the shell from ejecting all the way. You could probably rack the slide for follow-up shots, IF a shell hasn't jammed, and IF you're not drowning.
Anyone know what kind of pistol Beckett uses? I'm reading Heat Rises
now and it says Nikki Heat uses a type of gun called a Sig-Sauer (which is a name I remember because for a while I thought people were saying "Six-Hour" when they mentioned it on cop shows), and I'd tend to expect that Beckett would use the same since the character's based on her, but I can't tell by looking.