Reading over this, how many times can you actually explot this particular ascended trait? Can you only add/increase the psychic powers and Psy Ratings once or multiple times?

My reading is you can take it multiple times. As a GM I'd cap the max psi to 1 under what a Primaris Psyjer could have. Honestly it seems like a bad idea to go this route. As every thing costs more, and you lack the Psykana Failsafes. Plus a strict reading of p 124 would indicate that only Primaris psykers can do the Fettered/Unfettered/Push levels of power.

So by RAW you could buy your PSI up to dizzying heights as an Inquisitor or Intergator. (This is prime errata fodder.) But you'd be eaten the warp in pretty short order rolling that many dice. Personally as a GM I'd let a PC be an Inquisitor and take a career as a Primaris Psyker. Or reasonably cap the max PSI below that of a Primaris, and let the PC use the Levels of Power Chart 5-1. (Personally if I run a DH game I'm letting anyone use it.)

According to FF, you can only take each elite advance one time.