February combinations

For this month I prepared some combinations which have unexpected solutions, but are not so hard to solve.
Some of them are from my games, and others are from my database on combinations.
The first one is the combination that I failed to solve.
Black is on move, and the question is:
How do you evaluate a chances after 1...Rxd4 ?
Is White better?
Is Black better, or maybe the position is equal after some Ne2-Ng3 perpetual?
Calculate, and you will see.
This combination has very clear solution that does not leave a place for speculations.

This is the combination that I managed to solve.
Black is on move.
He has not so great choice and being piece down he has to trow in some checks.
Is it enough for a draw?
Maybe there is more then a draw ?
Do not dismiss the possibility that White can avoid all checks and win the game.
This is clear example of accurate calculation.
Combinational vision is not what you need to use in this example, just pure and organised calculation.

White is on move.
His king is under attack, but he has a piece for three pawns, and he can take one more piece on e5.
Or can he?
Find the best continuation for White.

This position is from my own game.
I was playing for GM norm (should I win this game I could lose in the last round, in Bosna Open 2011), and I sacrificed three pieces!
I got one back, and I got three pawns for the second.
The third piece is just matter of time, as two of Black´s pieces are hanging.
Find the best move for Black.

This is the position from the same tournament as the previous position.
I was Black, and I was again the second best player in the game.
White is on move and he tries to keep alive his dying initiative.
As a matter of fact, he has much more then keeping the initiative in this position, but he has to look deeper, far from obvious solutions.
White succeeded in this, and you can try to do that too.