Can an infant baby of 3 months old be teething?

Yes. Infants this young can certainly teeth. However, if they're having a high fever or very irritable or not eating, they should be seen by their regular doctor. At 3 months of age, their immune system is still immature and we wouldn't want to miss an infection that was blamed on teething.
Yes. Infants vary at the age that they start teething. Certainly not out of the ordinary.
Yes. Most babies get their first teeth around 4-6 months, but anywhere from 3-9 months is common.