One of Starship’s engines on the lowest setting would tear the station apart. Regardless of whether they make this based on Starship instead of something more reasonably sized like a Dragon or Falcon 2nd stage, it’ll still need either a new engine design or a big cluster of Dracos. It’ll be something custom.

Regarding their Artemis work- the payments are milestone based, so they get money as they pass milestones. Engine relights and ship to ship prop transfer are some of the next ones.

Regarding their other customers- the Starship manifest includes another moon cruise, several satellite launches, and a lot of Starlinks.