Architecture

With 166 marks in JEE Mains paper 2 you are not eligible to get admission in any good government/private college because they consider a score of above 300 marks in JEE Mains paper 2 for admission.

Your chances are null of getting admission in any government college with 221 marks in JEE Mains paper 2.
Above 300 marks are considered good for admission in a government college.

Considering your NATA and JEE Mains paper 2 there are zero chances of getting admission in any government college for B.Arch.
However, you may get admission in any private university/college with your score.

Hi,
For AAT (Architecture Aptitude Test) you need to clear 4 exams namely JEE Mains papers 1&2, JEE Advanced and then you need to clear AAT to get admission for B.Arch in IITs.
So if you have cleared all these only then you can give AAT. Only with JEE Mains paper 2, you will be eligible for admission

Colleges like SPA-D, NITT are better for B.Arch in my opinion. However, the college that you have mentioned are also good.

It's quite possible. Make sure that you give the option properly and have a good back up also.
All the best.

I can't exactly tell you if she'd get in or not considering that the cut off changes every year. You can however check in the internet to see the cutoffs for previous years and make a decision accordingly.