what exactly is teamfight tactics?i thought its splitpush or all mid?

It's DotA Auto Chess but League as far as we know.

It's an additional game mode.

it's a new game mode but probably too different from league to share the client so it will be a new game so Riot Games can earn it's S

Where can we find it? When can we find it?

We lost Nexus Blitz for this....

I guess they saw $$$$$$ signs and wanted to profit from autochess.