No. Eleven weeks is too early for teething. So, if an eleven week old is fussy as if he were teething, he should be seen by the doctor. The doctor will look for the real reason why the baby is fussing.
Highly improbable. But does happen rarely. If you see a raised white area may be eruption cyst or enamel pearl, self limiting occurrences. More probable that your daughter has discovered her mouth and is exploring. To be sure, see your pediatrician or take your daughter to see a pedodontist, a pediatric dental specialist.
Yes. Although babies can be born with teeth, it is unusual to be teething at 11 weeks. More likely, she has just started to chew and is enjoying putting her hands in her mouth.
Yes. Yes, it is possible. Some infants are even born with teeth. Others don't get there first teeth until after their first birthday. The most important thing at this point is to keep your baby comfortable. Find out what he or she likes to chew on while teething. Try items of several textures and temperatures. Each child is delightfully different.