Can DC 75th Deadshot use the Trick Shot feat?

If yes, then when can he use the benefits of Trick Shot? Would it only be when his power is activated by being in hindering terrain with no action tokens? Or would he be able to use Trick Shot whenever the special power is showing on his dial?

Yes, he can be assigned Trick Shot since his SP allows him to use RCE.
And yes, he will only be able to use the feat if he has no action tokens and he's occupying hindering terrain, since if those conditions are not met he cannot use RCE at all.
Note that he wouldn't have to actually use RCE to benefit from the feat, only to be able to do it.

Captain Krueger is correct.

Thanks for the quick reply.