Only thing we get from Tribble is the Tribble Test reward that will be given to us a few weeks after Season 7 assuming we qualify for it. Transferring tribble characters to holodeck would be a huge exploit since there is the problem of creating copies of your character to transfer EC and dilithium over to one and certain exploits from previous patches that would give unfair advantages.
no. these two servers are totally separate. the stuff will stay on the test server as is, but it will be brand new when holodeck comes.
you can copy to the test server but they will never allow people to copy back to holodeck, for the risk of bringing unstable code/bugs along for the ride and because often what happens on the test server can be radically different to how its meant to be played. this could potentially give testers an unfair advantage.