1 I don't even remember the last time I played chess, but...

Pawn E2 to E4. 
If Black Rook (E8) takes Pawn E4, take the rook with Pawn at F3.  Checkmate.
Any other move by Black, move Knight C1 to E2.  Checkmate.

2 Hm.  Just realized there's a counter: Bishop D8 to G1, allowing King to move F4 to E5.

Okay... how about... Queen H5 to H6, check.  Black's only move is King F4 to E5.  Move Rook H2 to H5.  Checkmate.

3 Err: the counter was Bishop D8 to G5, not G1, obviously.

4 Damn, same counter.  *sigh*  See, told you I hadn't played in a long time.

So if Black moves Bishop D8 to G5 to counter (instead of moving King), move Rook to H4 instead of H5.  Check and mate.

5 No!  If the King moves instead of countering with Bishop, don't move the Rook.  Move the Pawn F3 to F4.  Checkmate.
I should probably stop commenting now.  I think that's a pretty solid solution.

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10   Black's only move is King F4 to E5.  Move Rook H2 to H5.  Checkmate.

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