Yes, heirs have a right to see the will and to know everything about the assets and distributions. Yes, some personal effects can be distributed before the “will closes” or the probate is closed.
Florida probate laws include many protections for the beneficiaries of a probate estate. If you are a beneficiary under a Florida Will and there are assets that were required go through probate, you should have received some notifications.
You should require that the Custodian of the will deposit it with the court. If they refuse, they can be ordered to by the court and are subject to reimbursement of your legal fees.
Note, in Florida you do not have any right to see a will while they are still alive.