After getting passport, should inform respective consulate about the new passport?

What if older passport has valid visa stamps on it, especially US h1/ H4/Student visas on it. Do I need to have visit visa to go to my own country now? Can I apply for visit visa at Canadian consulate in USA?

How to manage this situation? What passport should I show while crossing the border especially to US.

Any body suggest information, Good source to find this kind of info.


Thanks in advance