are there actions that you can do twice with The same ship in a turn?

Currently, there is no way to do the same ACTION twice in a turn. So, if you take the focus action, then some other effect lets you take a free focus action, you can't take that free action. Night Beast allows you to get a free focus action if you make a green maneuver, so you couldn't then take a focus action. You can get multiple tokens however. For example, recon specialist lets you get two tokens for taking a focus action. Soontir Fel gives you a free focus TOKEN if he gets a stress token, so he could focus, then activate Push The Limit which gives him a stress token and a second focus token, but that's not an action.

are there actions that you can do twice with The same ship in a turn?

Nope, but there are ways to approximate it.

When an effect gives you a token, rather than a free action, you can get as many as the rules let you get. (E.G. if Soontir Fel somehow got 5 stress tokens in a turn, he'd have 5 focus tokens.