I have 2 questions.
1) Does this dialogue look natural? Any mistakes?
2) Do Brits say "What are you studying?" instead of "What's your major?" (As far as I know it's an American equivalent) talking about studying at university.

The dialogue:
A: What do you do?
B:I'm a five-year student at a medical university.
A: Amazing! What are you studying?
B: I'm studying nursing.

Thank you so much in advance 🥺🙏🏻

Question

I have 2 questions. 
1) Does this dialogue look natural? Any mistakes? 
2) Do Brits say "What are you studying?" instead of "What's your major?" (As far as I know it's an American equivalent) talking about studying at university.

The dialogue: 
A: What do you do?
B:I'm a five-year student at a medical university.
A: Amazing! What are you studying? 
B: I'm studying nursing.

Thank you so much in advance 🥺🙏🏻

Answer

Alina, 
You are right, we ask "What are you studying?".
"I'm a five-year student at a medical university" sounds a little unnatural to me. We would probably leave out the words "five-year", ("I'm a student at a medical university") or even just say "I'm a student"/ "I'm a medical student"/"I'm at university".
Victoria

Answer

In the U.S. we don't say "medical university". Instead, we say "medical school" or "med school".  For us, a university is a gigantic institution that contains all sorts of "schools", one of which might be a med school.

Answer

Do you mean ‘fifth-year student’  i e  a student in year 5 of the course ?
‘ What are you studying ?’  is fine.