The “summoning sickness” rule applies to {Q}. If a creature with an {Q} ability hasn’t been under your control since your most recent turn began, you can’t activate that ability. Ignore this rule if the creature also has haste.

If the permanent is already untapped, you can’t activate its {Q} ability. That’s because you can’t pay the “Untap this permanent” cost.

When you activate an {Q} ability, you untap the creature with that ability as a cost. The untap can’t be responded to. (The actual ability can be responded to, of course.)