I owe a mortgage on my home. Can this property be bequeathed to my beneficiaries?

Yes, the house can be bequeathed to your children, subject to the continuing lien of the mortgage. However, it is more than likely that the mortgage provides that the debt must be paid upon the death of the mortgagor (borrower).

Yes. The children must continue to make the payments. The Garn-St. Germain Act provides that heirs may continue to make payments without fear of accelleration due to change in ownership. If they don't make the payments, the lender can foreclose.

Please consult with an Attorney in your area that does both Probate and Real Estate there are many considerations here that need to be addressed