Patchwork Crawler 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; they have colons in their reminder text.

If an activated ability of a card in exile references the card it's printed on by name, treat Patchwork Crawler's version of that ability as though it referenced Patchwork Crawler by name instead.

If you control more than one Patchwork Crawler, each will have only the activated abilities of creature cards exiled with that specific Patchwork Crawler.

Once Patchwork Crawler leaves the battlefield, it will no longer have the activated abilities of the creature cards exiled with it. If it returns to the battlefield, it will be a new Patchwork Crawler with no connection to those exiled cards.

If Patchwork Crawler exiles a double-faced card, it will have the activated abilities of only the front face of that exiled card.