No, the Trustee holds the property on behalf of the Trust.
Only your attorney or accountant can answer that question. Some common reasons for holding property in a Trust are to minimize or postpone death taxes, to avoid a time consuming probate, and/or to shield property from attack by certain unsecured creditors.
Married persons can usually exempt a significant part of their assets from taxation and may postpone taxes after the first of them to die passes. You should check with your attorney or accountant before taking any action.
Yes, if the property otherwise qualifies.
A Trustee can take any action permitted by the terms of the Trust, and the typical Trust Agreement does give the Trustee the authority to borrow and encumber real property. However, not all lenders will lend on a property held in trust, so check with your lender first.
Some people who do not wish their names to show as titleholders make private arrangements with a third party Trustee; however, such an arrangement may be illegal, and is always inadvisable because the Trustee of record is the only one who is empowered to convey, or borrow against, the property, and a Title Insurer cannot protect you from a Trustee who is not acting in accordance with your wishes despite the existence of a private agreement you have with the Trustee.