Activated abilities contain a colon. They're generally written "[Cost]: [Effect]." Some keywords are activated abilities and will have colons in their reminder text.
No abilities of creatures your opponents control can be activated, including mana abilities.
Linvala's last ability affects only creatures on the battlefield. Activated abilities that work in other zones (such as bloodrush or unearth) can still be activated. Triggered abilities (starting with "when," "whenever," or "at") are unaffected.