1) A very obvious flaw would be a twist in the neck. Try to look from an angle like this:
View attachment 4354703
This is a good example for a twisted neck. If it looks like this, run away!
2) The neck has to have some relief. How much is a matter of preference. If you prefer very low action and play with a light touch, it can be rather flat. If you dign in heavily, you might prefer more of a bow. The ideal setup for you feels comfortable and easy to play and is buzz-free. It should at least be possible to set up pretty low action without fret buzz.
3) Have you confirmed that the bass has a truss rod? AFAIK, not all graphite necks do. If it does, I would expect its effect on a graphite neck to be rather limited. If the neck isn't close to where you want it to be, the truss rod probably won't get you there.
4) Very little. Graphite necks are a lot more stable than wood necks.
Take some time with the bass, and see if you can set it up how you like it. If that's not possible, I doubt that the truss rod or different string gauges will get you there. If you don't know how to set up a bass yet, now would be a good time to learn. It's really not hard if you know what you're doing.