I suggest (and highly recommend) to add new type of chess here - they called "battle chess".
The point in battles is intial full setup of board by both players:
white player setups white side, black - black and then game starts. It's like Shredder, but much better. You use any position you want, complete freedom and totally unexpected gameplay from the very first turn. There is site for them already, but rather bugged. Really wish to see them anywhere else, and here too.
So.. is this like chess960 with players getting to choose their own position?
The reason Chess960 is good is because of the randomness -- it makes it impossible to prepare openings. In this, you can prepare, which negates the whole point of Chess960 in the first place.
(I'm not in favor of this idea.)
What about black choose white setup and white choose black setup?
The side who chooses second yould counter the opponent's setup and would be at an advantage. It's only viable, I think, if pieces are placed in turns. There is some depth potentially in setting up your pieces that 960, or any symmetrical variant, doesn't have. Of course, your opponent can always still mirror your setup and it will be just the same. At any rate, I don't think this will be implemented because it's too similar to chess960 (and regular chess for that matter). New variants so far have always been considerably different from all other current variants.
No no no, you can't see opponent side of board before game! Think about it! NO openings at all - you have no idea what setup your opponent will have. It's much more like real battle - you understand enemy position only when battle begins. I beg you to try this
http://www.battle-chess.com and then request same type of game here, on lichess. Just try!
As for the fairness - game can be played two times: first, you use your setup, next you use opponent's and he uses yours. This way if one position has huge advantage, result will generally be 1-1. But if players are different, game may become even more interesting for both of them.
I don't think that's particularly balanced. It's very easy to randomly get a worse starting position this way. Basically, it's 960 with a handicap for one side. There's a reason why in tabletops you aren't usually allowed to hide both your army list and your setup from the opponent. Sure, statistically the results will be 1-1 after many games, but that doesn't make single biased games more fun.
The bias might not be apparent to many players, but I think strong 960 players could easily exploit opening advantages in this variant.
Hardly, 960 still have very limited start with poons&knights first to go. In free setup, standart turns are skipped from the very begining and positions can be almost unreal for standart chess. More complicated, more interesting.
But it turns chess (at least partially) into a game of luck. I don't think lichess will add the variant because of that.