Why can’t the fifa the player play for Tahiti

You are on loan. You can hand in a transfer request once you're back at the normal club. You can't be transferred while being on loan.

How to transfer:

My Pro -> My Actions

There is no way to increase other teams budget. You should try to get your player away from the club.

You should have thought this through. Though you can just wait till your contract has expired so people can get you for free. You can also ask your club if you can go out on a loan in the meanwhile or just ask them to put you on the transferlist so they sell you for probably less than they want to sell you. Though as a pro in career mode you should just sign short contracts if you're good enough to go to other clubs. Don't sign a 5 year contract.