Two questions. Will it be an issue if I go to my friends house with my laptop and play diablo 2 from there? Also I bought a new PC, will I be able to use the same diablo 2 account? Thank you.
Neither of those things would be a problem.
You can play from another location without issue and you can still connect to your account on your new PC 
Awesome, thank you so much for your brief reply, Schwayjeck!