I have C1 grade, is there any possibility of getting onsite

Yes, if you are a pro in what you do and your dependency in your project is substantial, the. You can go to onsite. You need to convince your manager as there will be an exception approval required from RMG head. I was at onsite UK and C1 to C2 promotion happened there only.

Possible for near shore. Onsite is highly unlikely

Difficult for US, European projects as far as I know

No