Heirs and Beneficiaries: Separate Property, Life Estate and Heirs

My question involves estate proceedings in the state of: Texas

1. A grandparent has separate property (mineral interest) inherited from their parent.

Grandparent dies intestate (after Sept 1993). Who gets what interest if:
a) a child predeceases the grandparent and leaves a surviving spouse and children?
b) a child dies after both parents and leaves a surviving spouse and children?

Does the surviving spouse of this child get a life estate or does it pass directly to the grandchildren?
Can this life estate be sold by the surviving spouse?
Can the child's surviving spouse (and holder of said life estate) sell the interest inherited by a minor grandchild? Would the life estate interest that would have passed to the child in the future also be conveyed in said deed?

2. A person dies testate and leaves residual estate equally to four children. Over a year later, the executor executes a lease, but not the four heirs. Why would the executor still be serving in that capacity instead of the children executing leases? When does the torch pass to the heirs? Does the executor have to convey/distribute by deed the interest to the heirs for it to be effective?

Heirs and Beneficiaries: Separate Property, Life Estate and Heirs