Is it possible for a sheltered/inexperienced person to be wise and mature?

Depends on what kind of maturity you are relating to. If its social maturity then yes you have to interact with other people to develop it. Wisdom is gained by a combination of both experience and knowledge so if you stay cooped up inside and withdrawn your wisdom in the long run will be limited. Maturity comes with age , generally, however many people never gain maturity despite their age.

yes and no.

perhaps the experience you talk of could come from a previous life?

Reading and learning at home can teach you a lot.

Sport and work means you may only encounter people of the same mind who do not think beyond the store or pitch.

The internet can teach you lots.

anyway thats my opinion only. I used to live in a small village with little opportunity to do anything new but always knew there was more to life outside the village.

peace and love

Being wise, or wisdom is acquired from experience. Maturity is knowing how to handle the tougher situations in life. So I'd say know, someone who is shelter barely faces tough situations and has not had much experience at all out in the real world.