"What is Tournaments Mode going to be like?"
It is still in development, but here there is a ZAPSAYOR's comment on PFE's official subreddit:
"You get to choose any Pokemon you like, and you can fight In certain modes with other players. Some Pokemon are banned like certain specials and legends. You can only use status effects during battle. Tournament mode will most likely come out after the MU."

Also, Uglypoe told some information about the Tournaments Mode on Discord:
"There are 3 different options in Tournament Mode: Solo Queue, Friend Queue, and Official Tournaments. Solo and Friend put you into public matches, and can be done at any time, Official tournaments are hosted by staff members.You'll get rewards for any option Though you'll only get the legendary mega stones in official tournaments."

"Couldn't a group of friends get together and each farm each other?"
Poe replied, "Not like that. Imagine it more like this: you go into friends mode, invite a friend or two and then that entire group is put into the queue against a randomly made/another friend group. It's not friends vs friends, it's friends vs randoms. Halloween Specials won't be obtainable in the tournament mode.Tournament Mode will have its own set of rewards."

Confirmed Rewards

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