Can you travel to Europe or America on a uk student visa?

A student visa has NOTHING to do with your ability to travel to other countries.

Your student visa simply allows you to live in the UK while you are studying.

If you want to travel abroad, you need a current passport and, if necessary, the correct tourist visa for the country you wish to visit.

No. Your UK student visa ONLY allows you to enter & remain in UK, as long as you are currently attending classes there full-time. You have NO privileges to any other country. UK issued the visa, so it's only good in UK. IF you are fulfilling all terms & requirements of that visa.

No.  You cannot even legally travel to Ireland as an Indian passport holder with a UK student visa. 

https://skyteam.traveldoc.aero/

Visa requirements for Indian citizens:

https://en.wikipedia.org/wiki/Visa_requirements_fo...

Note that universities normally help international students obtain visas.  Talk to the Office of International Students once you are at the university. 

No, your life is very resticted on a student visa, don't travel or make babies while on a student visa. 

A UK visa is only pertinent to the UK. Contrary to what some seem to believe not all developed nations share freedom of travel or honor each other's national visas. 

Your UK student visa allows you to ENTER/LIVE/STUDY in the UK for the term of your study ONLY.......... it has zero to do with visiting other countries....... you are a national of another country, if you required a visa before you got the student visa you still require one now......... and with covid you will not be travelling anyway

Obviously not. A UK student visa is valid and relevant only in the UK. 

if you want to travel anywhere else, you'll need whatever visa is required for your citizenship.