Can a person make niyyah for Qadah of a missed fasts and also do niyyah for Shawwal 6 fasts ?

Question1
No, they have to be kept separately. This can be deduced by a Fiqhi principle that if a person made 2 intentions whilst executing 1 Fardh act, the Niyyat for the stronger Fardh act will be considered, for example, a person intends to keep a Qadhaa fast and Kaffaarah fast at the same time, the Qadhaa will be considered fulfilled and not the Kaffaarah. (Ashbaah wan Nazaair vol.1 pg.45; Karachi)

Hence, in the case of a Fardh fast and Nafl fast, the stronger between the two, Fardh will be considered.

Question 2
Such a person will have to fast for 6 1 days (60 Kaffaarah and 1 Qadhaa). The 60 Kaffaarah fasts must be kept consecutively. If he is unnable to do so for a valid Shar?ee reason, e.g. continuous sickness, etc. then he has to feed to feed 60 poor people. He will have the option of choosing one of the following methods of executing his Kaffaara: a) Feed 60 poor people to their fill for 2 meals
b) Feed 1 poor person 2 meals a day for 60 days.
c) Give 60 poor persons 3.5 lbs (approx. 1.6 kg.) of wheat and rice or its value in cash or food grains. d) Give 1 poor person 3.5 lbs approx. 1.6 kg.) of wheat, rice or food, grains, etc. or its value in cash for 60 days. (Ta?leemul Haqq)

and Allah Ta'ala Knows Best

Mufti Ebrahim Desai