“Is there such a thing as frum/Yeshivish doctors?”
I like to think so. And I definitely know of many frum doctors,
” Can one actually go to med school and still make time to learn Torah (at least 2 hours a day),”
Yes though 2 hours every day is hard (certainly day before final that takes real motivation but certainly not impossible and not limited to medicine)
make it to minyan and daven three times a day?
minyan – impossible to be done everyday especially as a student and trainee
davening – can be done
“What does it look like when they need to enter an internship program and live as a frum Jew at the same time? Are there certain areas where on has to compromise on? ”
Minyan is a big one, davening in general is hard and especially as a student have to rely on bedieveds like Shacharis before neitz. Tefilin before misheyakir (R’ Moshe allows this but not lecatchila and not all agree)
I dont see how it is possible to avoid shaking women’s hands (there are mekilim but as is well known There are those who hold its yeharog Ve’al yaavor so I suppose that too is a compromise.)
though none of these are limited to medicine per se.
“What is their lifestyle like?”
Too vague.
Note the above is a generalization depends on stage of training and specialty matters as well