Setting up of firm/company

Yes,

All of 3 can start any of the constitution that you want. Be it Private Limited Company/ Partnership/ LLP.

The relavant provision needs to be complied.

The choice of constitution depends on your choice.

Private Limited is better for corporate image.

Partnership firm is better for simple and cost effective solutions.

LLP is middle way for both.

Profit repartriation and sharing for foreign national person depends on sharing ratio and other relavent details .

Regards