Tooth abscess and gum abscess? Could one have caused the other?

Yes. A gum abscess, if left untreated, may destroy the supporting bone loss and eventually involved the bone around the apex, then the bacteria would have access to the nerve via the apex and cause tooth abscess (endodontal abscess). This is called perio-endo lesion. A tooth abscess, if left untreated, cause pulpal necrosis, cystic formation, drainage to the gum tissue causing gum abcess (endo-perio).
Dental abscess. Certainly, a dental abscess can involve the gum by extension of the disease process, which originally began in the tooth itself.
It's possible. It's called an endo/perio lesion when one is linked to the other.

Related Questions

Pain as one symtom is more prevalent in a tooth abscess, gum abscess or gum cyst?

Why are you asking? Any one of those conditions can cause pain, depending upon how severe it is and its location. Is your dentist having difficulty diagnosing something that is causing you pain? Are you trying to self diagnose your pain? What you ask is not easily answered in this type of forum. See a dentist for an accurate and thorough answer. Seek a second opinion if necessary. Read more...
Tooth abscess. All abscess hurts if it could not drain. Gum abscess usually can be drain from the side of the tooth. Gum cyst would almost never hurts unless it grows so large in size. Tooth abscess, if not drained, would hurt the most. Read more...

Is it possible to have tooth abscess but have no lump on the gums?

Abcess. Yes. Sometimes the infection will drain towards the gums and create the "bump" you referred to. Other times the infection stays in the jawbone and does not drain to the outside. Read more...
Yes. Sometimes, infections do not have any outward symptoms. Read more...

Can earaches be a symptom of infected gums or a tooth abscess?

Yes. Due to the proximity of the ear to the mouth, and the distribution of nerves in the area, dental problems can often cause pain to radiate to the ears. Frankly, gum disease seldom hurts until an advanced stage (periodontal abscess). Tooth abscess frequently presents with ear pain. Also, "tmj" problems (from jaw joints or associated muscles) often causes chronic ear pain or ringing in ears. Read more...
Yes. . Infection of periodontal origin, "gums" or bone, or dental origin, "tooth abscess" in the mandible (lower jaw) will cause pain in the ear. See a dentist for diagnosis and treatment immediately. Read more...