Die Crew: Reist gemeinsam zum 9. Planeten

No — the sick crew member may not win a single trick (training/mission rule). See page 3.

Follow the mission text: some missions allow communication immediately, others forbid it until a specific trick (e.g. “only allowed to communicate starting with the 2nd trick” — page 5; “may not communicate until the start of the 3rd trick” — page 6 / page 8–9).

Yes — you may play 9-value cards, but you are not allowed to win any trick with a 9 (missions 16–17 explicitly state you cannot win a trick with a 9). See page 5.

You must arrange play so that the specified Rocket cards actually win tricks (for example, some missions require one trick to be won with each Rocket card — page 5; others require the Rocket cards to win in a specific order, e.g. 1 then 2 then 3 then 4 — page 10).

Right after the first trick is completed, every player draws one random card from the player on their right, then play continues normally (that exact procedure is written into the mission text). See page 4.

If the mission text says the Commander decides or distributes orders, the Commander assigns the person (multiple missions specify the Commander determines who repairs or who receives orders — see pages 4 and 6–7).