Harcourt Butler Technical University, Kanpur

No, I don't think so. Your rank should be around 100.

Yes, you can get good govt. colleges, be it NITs or autonomous institutes of your state where your admissions will be under home-state quota. Try for MANIT, MVNIT, NIT -Durgapur and NIT-Jamshedpur. Also, try for autonomous institutes of your state (which come under NIRF rankings under 100).
Best of luck.
Also, try it wtih predictor:
https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor?utm_source=connect&utm_medium=CR_JEECP&utm_campaign=7489993

Recorrecting your Exam name to UPSEE, you have excellent rank and you need not to worry. For HBTU, it takes through JEE Mains only. You can get into UP's top Universities such as UPTU's BIET Jhansi etc. and all such colleges accepting UPSEE.
PS : Kindly mention if the exam is different UPSEE . Best of luck and relax :)

Yes, you'll get into HBTU with this rank. Moreover, you'll not be able to get CSE for sure as the previous cutoff for HBTU CSE is too far from your rank so its likely to deviate. Moreover, you'll get branches such as Mech, BIOTECH , CIVIL, EEE , IT/ECE (less chances).
Best of luck.

Yes, you can get the desired college with your rank.

HBTU Kanpur will be a better choice as compared to Jaypee Noida. HBTU Kanpur holds better records than JIIT Noida.

You can go For JSS noida.