Re: MTG can tapped creatures use activated abilities which don’t require a tap? Yes. The only requirements to play an activated ability is that you must be able to pay all costs and choose all targets (and the creature must not have summoning sickness if the cost includes the tap or untap symbol).

Can you use creature abilities right away?

Unless a card explicitly states that it can only be activated on your turn (USUALLY denoted by “play this ability only as a sorcery”) the ability on a creature can be used any time the player wants once the creature no longer has summoning sickness for creatures that have the tap symbol in their cost.

Can a creature be tapped to prevent its activated ability?

Only after you are done activating your creature’s ability does your opponent has a chance to play his tapping ability, but by that point your creature is already tapped, and tapping it won’t have any effect. If you do not have priority, then your opponent may choose to activate his tapping ability to tap your creature.

Can you tap a creature on the turn it comes out?

A creature that has the Haste ability can tap immediately, so unless you have a Reflex Sliver on the ‘field, you will not be able to tap a Gemhide Sliver for mana on the turn it comes out. There is a comprehensive rule citation, but basic questions should also have basic references.

What happens when a creature enters the battlefield?

Unlike other types of permanents, creatures enter the battlefield with “summoning sickness”: a creature can’t attack, or use an ability that has {T} in its cost, until it has started your turn on the battlefield under your control. You can block with a creature or activate its other abilities no matter how long it’s been on the battlefield.

Can a creature attack if its under its controller’s control?

A creature can’t attack unless it has been under its controller’s control continuously since his or her most recent turn began. This rule is informally called the “summoning sickness” rule. Ignore this rule for creatures with haste