star wars - What was that creature in Rogue One?

What was that creature used to interrogate Bodhi in Saw's hideout?

It was difficult to understand what Saw was saying.

Answer

This is the Bor Gullet.

Saw turned his head to signal the Tognath. “Bor Gullet,” Saw said.
“Bor Gullet?” Bodhi asked.

_{^{Rogue One: Official Novelisation}}

According to Slashfilm, the creature originally had a larger part in the early script but was relegated to appearing in a a single scene.

Bor Gullet, a telepathic cephalopod that Saw Gerrera uses to extract information from prisoners, was created by screenwriter Chris Weitz “as a way to get inside Jyn’s head.” He gives us a look at the original intention of the creature, revealing that the Bor Gullet is an “empath, he can understand exactly what you’re thinking, be he also feeds off emotion. He likes things like fear and sorrow and sadness. And joy, too.”

The alien was initially designed as an insect-like creature, but they decided to do with an octopod because “his tentacles could go around people’s necks and heads and into their ears.”

_{^{Chris Weitz Created Saw Gerrera’s Alien Interrogation Creature Bor Gullet}}

As to your supplementary questions, yes, it appears to be telepathic (or possible Force-using) and no, there's no indication one way or another as to whether it's native to Jedha.