months of hajj

Q: I am a makkah resident who has done umrah this year 1437. Insha Allah I will be doing my first hajj. I intent to do an umrah in zul qa'dah for my deceased grandmother (passed away yesterday). Since I am a Makkah resident having niyyat to do hajj; performing umrah for myself is not permitted. Is it permissible to do umrah for the deceased?

Q: If one performs Umrah in the month of Shawwaal or anytime thereafter during the months of Hajj (i.e. from the beginning of Shawwaal till the 10th of Zul Hijjah), will Hajj become fardh upon him?