A creature that “can't crew Vehicles” can't be tapped to pay the crew cost of a Vehicle.

Activated abilities contain a colon and appear in the form “[Cost]: [Effect].” Some keywords (such as equip) are activated abilities and will have colons in their reminder texts. Loyalty abilities of planeswalkers are also activated abilities.

Intercessor's Arrest doesn't stop static abilities from affecting the game, and it doesn't stop triggered abilities from triggering. It also doesn't stop mana abilities from being activated. Most activated abilities that produce mana as they resolve are mana abilities.