What countries are involved in the F-35 project ? I know USA and Britain are. Any others ?

Quite a few, here's what I found.

 

The international signatories -- the United Kingdom, Italy, the Netherlands, Turkey, Canada, Australia, Denmark and Norway -- have had direct input in the design phase of the aircraft and companies worldwide are participating in the F-35's development. More recently, Israel and Singapore have joined the F-35 program as security cooperative participants.

 

Currently, United States and United Kingdom sales alone account for nearly 2,600 aircraft and the Pentagon expects additional foreign purchases to be in the thousands.

Regarding thrust vectoring, it depends on how you look at it. It doesn't have thrust vectoring in the sense of being able to adjust the rear nozzle, but of course it has separate nozzles used for VTOL, which could presumably be used to modify its in-flight trajectory to exactly the same (or better) effect.