Question: Can a damaged Decimator use the reinforce action then use Tua to do a red reinforce action at the star of the engagement phase?

A ship can not perform the same action more than once during the round. Tua’s ability says to perform the action. This would be different if the ability said to “gain a reinforce token”

RR PG 3: There is no maximum limit to the number of actions a ship can perform over the course of a round, but a ship cannot perform the same action more than once during a single round, or perform an action it has failed this round.

No. A ship may only perform a particular action once per turn. Difficulty (white, red) doesn't not impact this limit.

There are some effects which "kind of" get around this. Some cards assign additional tokens, or instruct you to acquire a lock, or in the case of Anakin Skywalker in the N-1 instruct you to perform a barrel roll. One key thing: these all use the word "focus token" or "acquire a lock" or "barrel roll" instead of the symbol for the action.

Basically, if it uses the symbol, it's an action and cannot be used more than once per turn. If an effect uses words, it can cause action-like things to happen more than once per turn.

You also couldn't do it if you had a damaged sensor array, as the damage card means you can only perform focus actions.