I have Valid F1 status and visa. Could I travel and return to USA while TPS (for Nepal) is pending ?

If you have a valid multiple entry visa, you probably will not face any issue. However, there is always a but! But, be mindful that you may not...

I own 2 gas stations and can I sponsor a Italian citizen.

What do you mean by sponsoring? More information is needed.

As my colleagues stated, you need two.

Do these 3 weeks are counted as home country residency ? I mean, Do these 3 weeks count against the 2 years residency?

Sorry but add 3 more weeks to your residency.

Can i hire a lawyer to check my paper work before sending it in ?

You absolutely can and actually encouraged to do that. Good luck.

Seek help of immigration attorney. You do not want to go for an appeal afterward.

Can a illegal immigrant travel inside the US?

Yes you may. However, as my colleague mentioned it would be at your own risk.

I have both F1 and J1(2year HRR)stamps on my passport.After completion of my J1 visa,Can I travel to Canada and change my status

Please do not post duplicate questions.

Status of I-140 and H4 EAD during employment change

The attorney who filed or helped with I-140 can help you.

Change of status from j1 to F1

Yes. it is impossible for real. You need to apply from abroad.