I'm assuming that Dyne didn't lash out at the world as he could hear Elanor's voice in his head (real or imagined) telling him not to do it, the same as he said she was telling him not to hate Barret and that being why he didn't hunt him down:

Dyne
"I hear her voice, Eleanor's voice. Begging me... not to hate
your rotten guts."

Dyne
"That's why I didn't hunt you down..."

As for how he got up into the Gold Saucer, that seems to be something of a plothole. The indication offered is that Dyne didn't give permission to leave the prison period so much as he gave permission for them to go up and participate in a Chocobo race, which would grant them their freedom if they won:

Mr. Coates
"You want somethin'?"

Barret
"I want to go up."

Mr. Coates
"Like I told you before, you gotta get the Boss' permission, then
win the Chocobo....."

Barret
"Dyne's got his reasons an' can't speak."
"So, I got this instead."

::Barret shows him Elanor's pendant::

Mr. Coates
"Yeah, bull--!!"

Barret
"I want to go up."

Mr. Coates
"R, right."
"Did you kill Dyne?"
"You must've. Or you'd never be holding that thing."
"So Dyne's dead... Maybe now, the place'll calm down a little."
"Dyne didn't care who anyone was......"

Barret
"The hell do YOU know!!"

Mr. Coates
"R... ri.... right! I mean, no, I DON'T know anything.
S, s... sorry."

Cloud
"Then, will you get us outta here?"

Mr. Coates
"Huh? Oh man, you guys are mistaken."

Mr. Coates
"I already told you, there's only one way to get outta here."
"That's to win the Chocobo Race and that's help up there, in the
Gold Saucer."
Perhaps Dyne wasn't a prisoner there in the first place, and just chose to stay there? That way, if Dio was aware of him, he may not have felt he had reason to suspect him of the crime since he was always about, perhaps keeping the prisoners in-line?