Indore

Hello, I hope you are doing well. You can try for IPS Indore regarding your expectations.

No, you have very less chances with this score. Last year, the closing rank of this college was 86K.

MANIT is one of the top ranked NIT, whereas SGSITS is good autonomous institute. Still it depends what you are getting and what you chose. SGSITS CSE is definitely better option than MANIT mechanical or chemical. Ranking wise, NIT - Bhopal is way better.

Kindly follow my answer below:
https://ask.shiksha.com/what-is-the-cut-off-rank-home-state-quota-for-general-category-candidates-in-sgsits-qna-4105847

If you are getting core branch in GSITS even after home state quota, then don't go for lower NIT's as then GSITS will be better. Things are not only dependent on the NITs, also, GSITS has mostly NIT type student quality and sincere curriculum. I would strongly recommend you to go for GSITS.

In around 2013, Microsoft first time recruited from Madhya Pradesh and they decided to come on campus at GSITS Indore. Also, they recruited 7 from GSITS, one with 24 LPA which is the highest till date.

Kindly refer to my answer on the similar question:
https://ask.shiksha.com/i-had-111-in-jee-mains-2016-and-95-pcm-aggregate-i-belong-to-general-category-can-i-get-sgsits-college-of-Indore-qna-3654018

You need to clear JEE Mains with the valid cutoff to be able to stand for a seat in GSITS. Kindly go below the link to know the cutoff.
https://ask.shiksha.com/what-is-the-cut-off-rank-home-state-quota-for-general-category-candidates-in-sgsits-qna-4105847
Now, you need to go through few rounds of JOSAA counselling similar to that of NIT's and IIT's and fill your desired choice. As you freeze your branch, you need to go for on campus verification and then you are admitted into the institute after few days of processing.

SGSITS Indore is not a private and government institute but is state government. Funded, supported but run by administered and maintained by private organisation. These colleges are called autonomous institutions which runs on both private and government interference.