Petroleum Engineering

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 :)

Both BE or B.Tech Petroleum Engineering are similar degrees. It's only nomenclature difference.

You should opt for science with mathematics in your 11th standard.