If i am Studying in canada as a Foreign student, can i go visit some other country?

Normally student visas are multiple entry visas so it is usually possible to depart and return without the need to apply for a new visa provided all other conditions remain for you to be allowed back to Canada. Both the study permit and temporary resident visa (if required for Canada) must be valid, and of course your passport also must be valid, when you seek to return from your summer vacations.

As far as visiting other countries you would have to meet the entry requirements for that individual country and the immigration authority for that country would determine if you meet them and if you do how long they would allow you to visit.

If you require a visitor visa for the US you need to apply for that in advance of planning to travel there.

It depends on what country you are a citizen of. Contact your embassy/consulate. Whatever country you have citizenship in will likely determine whether you need a visa as you don't have a Canadian passport..