1. Does my Mom become the complete owner of this property or does this property legally gets divided in to 4 shares (My mother and her 3 children meaning 25% each.)
Your mother is the owner of the half of the property and the balance half property shall devolve equally on all the legal heirs of your deceased father which includes your mother also.
2. If the 3 children have legal rights over this property does it mean that from their respective share (25% each) their respective spouse can lay any claim on this in case of a divorce.
The 3 children have rights in their deceased father's 50% share in the property along with their mother. Therefore the children will actually have 12.5% share in the property.
Their wards or spouses cannot claim any share from that during their lifetime.
3.If the 3 children have legal rights over this property does it mean that from their respective share (25% each) they can enter into a agreement and transfer complete and 100 % right to my mother.
The children can execute a registered release deed in favor of their mother relinquishing their rights in the property.
This will make their mother an absolute owner of the property.