My Homework from My coach

Hey, I thought I would post my homework for you all to take a look at it. I think I've sloved for sure three of the positions and am still mulling around the 4th.

1.) How should black play? Give the winning line if you can.

2. How should black proceed? Can he hope to win this this endgame?

3.) How do you evaluate thsi postion (who do you feel is better and why?)? In the game, White played Nd5. How will game continue after this, and do you make any modifications to your initial assessment. (this is the problem I am still mulling over)

and the 4th.

In this rook ending Anand decided to play 1...a2. Do you think this was the right devision? If so, what is his winning play. If not, how can white expect to draw?

I took a quick look at these earlier, bu thaven't really had time to dive in.  Is the first one 1. ...b6 2. b5 cxb5 3. Rxb5 4. Ba6?

I don't know the answers for sure, I haven't met back up with my coach yet; But I'll tell you I had a completely different answer to the first one.

I won't give it away unless you want me to.

Im thinking this may work.   For #1    1  ...Ne4            There are a couple of ways to answer this, but if their white bishop cant be taken off of its square because of a checkmate threat.  im sure there is a good way to answer this but so far i cant see any obvious one.    even after pawn takes knight, rook takes pawn, then black can sac his white bishop on g4 and hope to bring the rook to that square, putting pressure on the king.   Am i just not seeing how to respond to this?   Other than that i did see advancing the b pawn as a possiable answer.  (Before i saw heisters answer)

I definitely have the answer to the 2nd.  Do you want me to give it away?

I think i have 2 figured out.  

On the 3rd white has the better ending because of the queen side majority.  However, black has the better minor pieces.  So if the endgame is reached, white is better, but currently black is better.  After Nd5, a move that forces some trades(queen and probably at least one set of minor pieces), it looks like black's queen side pressure is gone unless there is a tactical shot.  So you could say that white is slightly better from the original position.

For #1 the answer beings with Bxg4. I'll let you all work out all the variation.

for #2 I am pretty sure black can win by bringing his king over to the king's side and breaking though over there. (let me know if this is your plan heister)

and #4 is a trivial win for black after a2. I can give you guys a sample line if you want, but I don't want to spoil it for anyone still trying to solve it.

i had the same for 2.   on 4...can white just bring his king over to the queen side staying on the 2nd row?   if the king moves off of that row he looses his rook.  its still pretty bad having to bring the king all the way to the other side of the board but its the only chance i see for white.

It was, but the method is the tricky part since white will try to blockade with a3 and not let the king penetrate.  You have to use a zugzwang (the bishop has to take a slightly odd path to do this).   

wha?