CBSE

Hi,
You can get some NITs like Goa, Manipur, Sikkim, Agartala, etc. and some IIITs but I think you may not get it in the first round of counselling.
You may refer the link below for the previous year closing and opening ranks:
http://josaa.nic.in/Result2016/result/OpeningClosingRank.aspx
This will not be the same this year but it may give you an idea of which colleges you may get.
The counselling registration starts from 15 June and the first round seat allotment is on June 28th. Refer www.josaa.nic.in.

Yes, you can get admission.

You can join nursing course only after completing 10+2.

It depends on the course and college you are looking for, but I think you might not be able to qualify the cut-offs.

You can solve RD Sharma or RS Agarwal book for maths and ABC for physics and chemistry. You may prefer YouTube videos lectures for better understanding.

No, at this rank you can't get admission in LNMIIT, Jaipur. Last year's cutoff was around 110. You can check colleges under JAC Chandigarh. All the colleges under JAC are very good except UIET regional campus Hosiyarpur.

Here is a link. You can check the expected cut off of the college on the basis of MH-CET score and check if you can get it:
https://www.shiksha.com/b-tech/resources/mhcet-cut-off-predictor