Would having a bottom tooth prematurely hit the left side of a top tooth cause soreness? Only half the tooth gets sore. Sometimes it even creates a tiny zap when eating but this is rare.

See a dentist. You seem to have a very good sense of your bite. However, there are problems with premature contacts including excessive wear of the tooth and possible change in the bone and gum tissue around the teeth involved. See a dentist to see how this prematurity can be corrected.
Premature contact. All tooth symptoms will be relieved after the occlusal adjustment by your dentist. Very common benign procedure.
Yes. As long as the tooth did not get knocked out your symptoms should improve in a day or so. The attachments that connect the tooth to the gum can get stretched and that can cause soreness.
Occlusal Problem. If your bite is off and a bottom tooth is hitting an upper tooth prematurely it can cause soreness. I would recommend you make an appointment with your dentist and have the area checked out. Your bite may just need to be adjusted or something else may be causing it. Prolonged premature hitting of the upper and lower tooth could lead to complications.
Dental Appointment. The solution depend on the severity, timing, and duration of your symptoms. You could need anything from rest (nothing) to orthodontics & surgery; likely something in-between. See your dentist, find the answer and feel better.
Hmmm. Several possibilities here: The premature contact could be the result of a habit, a malocclusion, gum problem, nerve problem or something else. See a dentist for a clinical exam, x-rays, bite analysis and appropriate treatment if needed and as required.
TMJ & Malocclusion. are contributory to this condition. Avoiding further trauma can help the nerve to recover. In the presence of bruxism and clenching habits, it can aggravate the condition and can lead from sensitivity to pulp necrosis.
Bite adjustment. Yous should see your dentist to have your bite checked and adjusted before it creates more issues.
Yes. See your dentist for analysis and adjustment to your bite.
It is not rare. If you are constantly putting too much pressure on that tooth it will aggravate the nerve and make it hypersensitive and always sore. The tiny zap could be nerve pain, especially if there is any crack in the enamel. Your dentist needs to make sure it does not hit too hard or the pain will continue and could even damage the nerve irreversibly.