Rex gains only activated abilities. It doesn't gain triggered abilities or static abilities. Activated abilities contain a colon. They're generally written "[Cost]: [Effect]." Some keywords are activated abilities and may have colons in their reminder text.

If an activated ability of a card in exile with a brain counter on it references the card it's printed on by name, treat Rex's version of that ability as though it referenced Rex, Cyber-Hound instead. For example, say Arcade Gannon (which has the ability "{T}: Draw a card, then discard a card. Put a quest counter on Arcade Gannon.") is in exile with a brain counter on it. You would treat Rex's version of the ability as though it said "{T}: Draw a card, then discard a card. Put a quest counter on Rex, Cyber-Hound."