1) If father dies during his service (just 5 day before)can daughter get his govt job, ?
First of all none can claim his father's job. Govt services an not inheritable.
One can claim compassionatge appointment and if found eligible and found best deserving enough within 5% of the Direct recuitment share on lowest level of GpC&D posts, he/she can be offered any available post clerk/peon/washman/waiter/cook/waterman/ sweeper.
daughter can also apply.
2) Even though if his mother is a govt employee , can daughter claim for it ?
if mother is govt employee then son/daughter is least likely to get compasssionate appointment because there is no starvation threat to the family.