Can legal heirs gift their share of an immovable ...

Yes, but I don't know how the tax situation would work.  If it's a small enough amount, it may not matter, but I believe there are limits to outright gifts between relatives and over a certain amount can trigger income taxes for the recipient.  As far as the original inheritance tax (if any) on the estate, I don't know if it sticks to the original heir or the recipient.  I would think that the recipient would willingly pay all the taxes as a gesture of gratitude.

Don't hesitate to ask another question in order to define your exact problem. 

Best advice is to ask a local lawyer.

Probate is the legal process of settling the estate of a deceased person, specifically resolving all claims and distributing the decedent's property. When one is said to have died “Testate” it means they died leaving a will. If one is said to have died “Intestate” there was no will left behind.

Making a will is not a way to avoid “probate,” the court procedure that changes the legal ownership of your property after your death. Probate makes sure it’s your last valid will, appoints the executor named in your will and supervises the executor’s work. You can do several things now that can help your executor and family later, hopefully much later on.

Generally, there are five purposes of estate administration, many of which have subsets to them:

            1. To determine that the descendent is, in fact, dead.

            2. To establish the validity of the will.

            3. To identify the heirs and devisees of the descendent.

            4. To settle any claims that creditors may have against the estate.

            5. To distribute the property.

An “executor” carries out the directions and requests set forth in the descendents will. An “administrator” is appointed by the court to manage the estate of a descendent who dies intestate.

Steps to a normal uncontested probate

1. Death of descendent.

            2. The will is delivered to the executor or Court Clerk.

            3. A petition is filed for the Probate of Wills or Letters of Administration.

            4. A hearing is held on the petition.

            5. Letters of Administration are issued by the Court.

            6. Notice to creditors is given.

            7. Inventory and appraisement of the estate is made by an independent probate appraiser.

            8. File Federal estate tax return. Return states “No Tax Due” or specifies an amount due.

            9. Final accounting and petition for distribution.

            10. Final decree of distribution.

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Yes but the transaction has to be done by the attourney on file of the estate.