Colleges in Noida

There are n number of colleges in Delhi and Noida, please specify a course or any stream, so that I can help you in a better way:
1. JNU
2. Delhi University ( for some courses)
3. Jamia Milia Islamia
4. Guru Gobind Singh Indraprastha University (semi-government. )
5. Delhi Technological University
6. AIIMS
7. IIT
8. Ambedkar University
And many other government colleges/Universities are available in Delhi which conducts Entrance exams for admission.

Yes, you can apply amity just simply filling there registration form which cost INR 1100/- and you can do it online in given link below:link-https://www.amity.edu/admission-procedure-domestic.aspx

The last date to apply for any UG course at Amity University, Noida is 13th June 2019. Many other colleges in Delhi offer bachelors in Political science.
Link to all the colleges is given below:
https://www.shiksha.com/humanities-social-sciences/political-science/colleges/colleges-india?rf=filters&ct[]=10223&uaf[]=location

Hello
You should visit this link for admission procedure.
https://www.shiksha.com/b-tech/course/b-tech-in-information-technology-jiit-jaypee-institute-of-information-technology-noida-23148
And you can use this link for finding other colleges also.
https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor
All the best

Yes, you can still apply for BHM course at Amity Gurugram by simply filling there application form which cost only INR 1100/-. You can also go to university's site (given link below)
link: https://www.amity.edu/admission-procedure-domestic.aspx

Yes, it will be a good option to pursue BJMC course in Amity but I don't think they have good placement record for this course.