JEE

yes you can also try VGU JAIPUR

apply to poornima university, Jecrc University and Vivekananda Global University

try VGU Jaipur or Galgotia

Yes a lot of colleges in Maharashtra accept JEE scores. You could also write NATA exams for B.Arch entrance. Some colleges even have a separate entrance exam after your NATA/JEE exam scores (even interviews).

Just for once go through whatever you have studied just to brush up on whatever u have studied. dont try to learn much new things new. try to do mock test and practice problems. dont get tensed. just utilize those 30 days as much as possible. practice as much problems as u can and equal time to all subjects.

For physics, try to complete HCV both parts and IRODOV. Also, you need to get some material from good coaching centers as they have the level that you need to prepare for JEE. For math, do complete RD Sharma class 11th and 12th and then differential calculus by Amit Agrawal, integral calculus by Amit Agarwal.

Solving class 11th or 12th or HCV won't help much for JEE. You need to get more tough content to practice. You need to get some practice materials from good coaching classes. Also, try referring books like, Irodov for physics.

Among these all, VIT is the best if you do not secure a NIT by your JEE Mains rank.

I think, you must prepare for both boards and JEE. You have to prepare for boards to get at least 75% marks, so that, you can appear in JEE advance.