Skill affects both. You can get the AI to pay you a tiny bit more with higher skill and bribery is a lot more successful usually (provided you have more than enough funds to bribe a unit in the first place)

As for what to do with him, he'd probably be good for bribing, but its overly expensive and most of the time it is not worth it.

High skill diplomats aren't as useful as high skill other agents in general. The difference in negotiations with a skill 0 vs a skill 10 diplomat are fairly negligible.