yes you can

since i am myself a BTech student in NIT, so as far as my knowledge is concerned and as far as i have researched and asked the authorities, it primarily depends on the college you are in  like its ranking and recognition. It has been seen mainly students from IITs and top NITs take advantage of such opportunities as their colleges are usually well recognized, even i have examples around me where students from top most IITs and NITs have done their research internships in universities such as Cambridge and Harvard soon after their 2nd year or 3rd semester which actually is a result of their college international MOUs. However students from other colleges where things like international MOUs are not provided by the college they can apply in NASA etc for internship however it is really tough to get internships in foreign in your ongoing bachelors.

Yes, B.tech students can apply and get foreign internships.

Some of the websites you can apply for foreign internships are -

1.IESEC (www.aiesec.in)

2.GoAbroad.com.

3.www.wemakescholars.com/

4.GoOverseas.com.

5.Work Your Way Around The World.

6.The Intern Group.

7.Cross-Cultural Solutions (CCS)

8.Global Vision International (GVI)

It is hard to get these internships as they only select interns with high industry experience and good skills.

Foreign Internships provide unique work environment and allow interns to meet people from different cultures.

Foreign internships are of 2 types - research and industrial

Internship is phase in which you are trained with skills you are good and apply your knowledge to industries.