Immigration Site

I currently live in US and will be getting my US residency soon.
I have been out-of-status here for most of my life but now my GC is pending. So, my citizenship is still with my home country which means my passport would be under that country as well. Now, if I want to travel aboard (as in once I get my GC), how does this work?

I have been out-of-status here for most of my life but now my GC is pending. So, my citizenship is still with my home country which means my passport would be under that country as well. Now, if I want to travel aboard (as in once I get my GC), how does this work? You travel under your national passport. Having a GC may or may not waive the need for a visa, depending on your citizenship and the country you are visiting.

You travel under your national passport. Having a GC may or may not waive the need for a visa, depending on your citizenship and the country you are visiting. Would my home country (which I have the only citizenship to) care about my "former illegal" status when I travel? Or does that just not really matter anymore..

Would my home country (which I have the only citizenship to) care about my "former illegal" status when I travel? Does your home country have laws against living in another country in violation of that other countrys laws?