Can abilities with no "tap/untap" cost be activated while a creature has summoning sickness?
Correct. Activated abilities may be used whenever you have priority as long as you can pay the cost and aren't forbidden to. The tap/untap symbol as part of the cost can prevent you (from summoning sickness). Having to use an ability restricted to sorcery speed can prevent you. Other than that (less any other restrictions), it's fair game.