Can a tooth remineralizeitself? if so, how?

Yes: Teeth are in a constant flux of mineralization and demineralization via the saliva. Very early stages of tooth decay (demineralization) can be reversed (remineralized) by positively changing the environment around the demineralized tooth thru improved hygiene, less carbonated drinks, less sugar intake, and reduced intake of acidic foods.

Damaged enamel : Can re-mineralize given the correct environment. Demineralization occurs in the presence of acid. Enamel can be "repaired" in the presence of Fluoride ions from toothpastes and other oral products. Clean teeth, healthy foods, and regular dental visits can minimize the demineralization issue. Don't expect large areas of damage to repair via remineralizaion. Fluoride can't fix everything.

Yes: But this it depends to amount of de-mineralization, if it is too much the answer is no and you need your dentist help to restore your tooth.

Yes: Teeth mineralize naturally through your neutral ph saliva. If you brush properly and reduce intake of carbonated beverages, sugary candy and mints. There are also prescription Fluoride meds that your dentist can prescribe to help remind rallies your teeth faster.