“What does an abscess tooth look like?”

An abscessed tooth doesn't necessarily look any different from a healthy tooth. It is dependent on what caused it to become abscessed. Most commonly extensive decay reaches the nerve and blood supply in the center of the tooth causing the tooth to die and an abscess (infected puss pocket) to form. These teeth will usually be black and/or broken. If the tooth died because of trauma, maybe by being hit in the case of a front tooth, it can die with the same resulting infection even though the tooth looks fine.

That depends on how much damage to the tooth structure. It may look severely broken down, or it may look perfectly normal (example: cracked tooth).

Abscess, you can't see it except if you did an X-ray.