Is there any list of all the different skills that bridge officers can have?

easy answer: on earth space dock, next to the BO-seller is a BO trainer. also look onto the BOs you were offered, they may have some other skill or mk of a skill

if youre looking for a spreadsheet use search, i saw one somewhere here yesterday

Does the trainer definitely have every single ability on offer?

well, for starters you can take a look at my guide, it's the last link in my sig, but I know for a fact theres a more detailed list that states what all skills are affect by what (but not the counters)

Here is a good list too:

http://stowiki.org/wiki/Bridge_officer_abilities