Rich pensaba que se las estaba arreglando...
 

Hi,

Rich pensaba que se las estaba arreglando muy
bien hasta que comenzaron los vómitos.

What is this las, and why plural?

Another instance of lexicalized pronouns

arreglárselas = cope, manage, get by (without any aid)

The original text is "Rich felt like he was doing pretty well until the vomiting started"

Again, problems with the translation. Arreglárselas implies Rich is the agent in a wide variety of situations (he copes, he manages) while be doing well implies he is getting better after an illness.

In my opinion, a more proper translation would be "Rich sintió que estaba mejorando sostenidamente, cuando comenzaron los vómitos" where cuando substitutes until implying the turn of the events