بسم الله الرحمن الرحيم
(1) Fatimah Kausar is good name. Fatimah means a weaning woman and Kausar is the name a special fountain in Jannah. We could not find the meaning of Fatimah which you have written.
(2) Both the names are good.
(3) Don’t prefix Aainah with Maryam, simply keep ‘Maryam’ it will be better.
(4) (1) Muhammad (2) Qasim, (3) Muhammad Ahmad (4) Muhammad Tayyab (5) Muhammad Tahir (6) Muhammad Ashraf (7) Muhammad Murtuza (8) Abdullah (9) Abdur Rahman (10) Razaur Rahman (11) Saeedur Rahman (12) Abu Obaidah.
Allah knows Best!
Darul Uloom Deoband