It is not acceptable to offer bananas with skin; we should offer them like how we eat. Some offer it by peeling just a part of the skin. In temples, it is not feasible to peel the entire skin of the fruit as it has to be given back to the devotees and Emperuman accepts it as well. But in houses, it is better to peel the skin and offer the banana. If there are lots of fruits, offer it according to convenience. If there are 12 bananas, peeling all of them would not be conducive as the fruit might attract flies.
Yes, fruits that are offered to Perumal can be given along with thamboolam to guests