Colleges in Rajasthan

Sorry, but with these marks, you won't be able to get into MVNIT with your rank. Also , it'll not be possible with any of the government institutes. Kindly go for private universities with B.Arch courses which have big placements records or try for a drop.
Recommendations are VIT, Manipal, Amity and

Though your marks are almost around MANIT B.Arch, you'll likely to get admission in second round possibly with hoem state quota.
Some recommedations are:
NIT-Bhopal, Calicut, Hamirpur, Jaipur, Nagpur, Patna, Raipur, Rourkela, Trichy, Kozhikode, Vnit. SPA - Vijayawada, Bhopal, Delhi, Bhopal. Mizoram Un

Yes, you are eligible for this college because it's a private college. JECRC college is the best but the university is also good.

No, B.Sc maths honors is not available in this institute. The course available is B.Sc maths only.

Yes Singhania University is authorised to conduct B.Sc. AME course. It carriers all the validity.

Apply online on http://jecrcuniversity.edu.in/ as soon as possible as the last date (may be extended) was 14th June 2018 only.

You have a chance. Go for it but it also depends if you are applying from home quota or other state.
All the best!

The students should score at least 45% in their 12th for this course.
12th
Aggregate of one language and three best elective subjects would be considered as best four subjects (BFS). Environmental Education (ISC), Fine Arts, Graphic Design, Painting, Dance, Music, Physical Education, Home Science, En

Bits Hyderabad should b your only preference as it is better than CET in all terms.