JEE

I'll suggest you to go for Mechanical engineering with automobile specialisation or simply switch to Automobile Engineering. If for any reason you don't get these go for CSE, ECE or electrical engineering in any of the so called proper campus IITs and do branch shifting later. Moreover, if you go to

Kindly mention your JEE Mains score, category and preferred state.

Please go through the following link for more clear ideas:
https://www.shiksha.com/b-tech/resources/jee-mains-cut-off-predictor

Kindly provide the information of your boards result and your preferred branch and state.

Sorry to say but you cannot get admission with this score in an architecture college because a score of above 90 is considered in NATA for admission in B.Arch in various government colleges.

Yes, you definitely can appear for IIT JEE if you clear cut-off for the eligibility. For that you have to appear for JEE Mains.

Depends on your interest. If you are interested in B.Arch, then go for its counselling, otherwise wait for MHCET rank, because your 34 marks will not let you to take admission in good college.

Hello Ashutosh,
Your rank is far beyond to get admission in any good private colleges, however you may get calls from various colleges to get admission there but trust me they are worthless, so figure out what went wrong and prepare well for next year.

You should try IET or HBTI because your marks in JEE Advanced and main is not enough to get good NIT and IIT. Although you may try JAC Chandigarh counselling. You may get UIET Punjab University which is far better than lower NITs.