these piece winning methods does not relate to fork or skewers!

In the first position, 1... Qxf1+ saves Black (in fact, he gets an advantageous ending).

Not, really Bishop+ knight vs Rook is a tie!

But, it is right that you think Black should play Qxf1 

Rook plus 2 connected passed pawns is better than bishop + knight.

these moves are not forced. in the first one, as stated, black plays 1...Qxf1+, entering an endgame with rook+two pawns vs bishop+knight. that's 7 points vs six, in case you don't know that. in the second, white just plays 2 h3 and has avoided mate, although black will win anyhow.

wat is a skewer...