After I play a character during the marshalling phase. Can I use his effect that turn if it is a marshalling effect?

Same question but with locations too. Like godswood.. Can I bring in in and then kneel it to get the bonus on the next stark i play?

Yes. There is no "summoning sickness" (to use old Magic terminology) in this game.

For a detailed discussion of timing of during the Marshalling Phase see this thread .