Petroleum Engineering

Kindly refer the below mentioned link:
http://entrance-exam.net/diploma-in-petroleum-engineering/

1. University of Texas Austin.
2. Stanford University.
3. Texas A&M University.
4. University of Tulsa.
5. Colorado School of Mines.
6. Pennsylvania State University.
7. University of Oklahoma.
8. Louisiana State University - Baton Rouge
9. University of Southern California.
10. New Mexico Institute of Mining and Technology.
11. Texas Tech University.
12. University of Kansas.
13. West Virginia University.
All the best.

If it's equivalent to B.Tech or BE in India, you may definitely do it. Check the details at institution of engineers to see how you can register.

BS in PE in USA is equivalent to B.Tech/ BE in India. You are eligible to do MS after BS is USA.

Both the institutes are equally good, but to know the exact scenario for faculty and placements, you should get in touch with the current students through social media or in person.

chem-pet is possible

B.Tech.chem-M.Tech.pet. possible

chemical-petroleum possible

Nowadays, petroleum engineering can be considered the best in comparison with mechanical engineering.
Petroleum engineering has more job opportunities as there are less students in petroleum engineering than mechanical engineering.
Also it's depend on your own interest.
If you have interest in Mechanical Engeneering then Mechanical Engeneering will be best for you !
All the Best :)