Uttarakhand

It is the best university in terms of placement but the university is too expensive.

Yes, DIT University is a recognised university, so yes you can go ahead.

Yes, why not. UPES, Dehradun is one of the good private college which has also top class facilities and top class teaching styles it has good placement records but fee is high. So, if you are not getting any other good college then you may go through this college for B.Tech.

You may refer to the following link for the ranking of IITs:
https://www.shiksha.com/b-tech/ranking/top-engineering-colleges-in-india/44-2-0-0-0

I would suggest not to concentrate more on the cheaper colleges. I agree, these days, the cost of education is very high. You cannot get affordable and best colleges together. The cheaper colleges are not good in terms of faculty campus and placements. The expensive ones are much better.
You can go for DU and JMI colleges in Delhi. They have comparatively lesser fee structure as compared to the private one.

Graphic Era, DIT, Uttaranchal Institute Of Technology, College of Engineering, Roorkee are some good colleges according to your rank and marks.