Puzzle of the week #273

Black has been under a heavy attack the whole game and managed to survive so far; now it intends to to give up the Rook for a chance at a perpetual check escape with Qd6-d1-f3-h5+. If black manages to do it, there is no escape from it and the game will end up in a draw. White to move; your tasks:
a) Analyse the position and decide if white should accept the draw or not
b) If you choose to go for the draw, please write the solution starting with 1.Nxf7 Qd1+
c) If you choose to play something else, please write the best line for white you can think of
Total available points for this puzzle is 30 if you choose to answer to all questions anyway. The answers will be published next time together with puzzle #274.

Puzzle #272 solution:
Game Soultanbeieff - Borodin, Brussels 1943. Cody's answer:
"a) Absolute pin on Rf3
b) White stands better
Material: equal
Kings position
- White king only can move on g2
- Blacks king is trapped in the corner
Pieces
- Whites rook on f3 is pinned
- Whites rook on g1 is on a open file
- White has double pawns
- 2 of Blacks major pieces are on the back rank
- Blacks queen can't leave the back rank or else Qxf8#
- Blacks bishop can't leave the d4-g7 diagonal or else Qg7#
- Black has 2 pawn chains
[Event "Puzzle #272"][Date "2015.03.10"][Result "1-0"][SetUp "1"][FEN "q4r1k/5p1p/p2pp2Q/1p2b3/8/2P2R2/P1P4P/6RK w - - 0 1"]1.Rg2!! Rg8 (1...Qd8 2.Rh3 {Followed by mate}) (1...Qxf3 2.Qxf8#) (1...Bg7 2.Qxg7#) 2.Qxh7+ Kxh7 3.Rh3#

Correct solutions:
Cody, Jalen, Hyson, Bradley - 20 points
Coco, Yakov - 15 points
Benjamin, Deryk - 10 points
Aaron - 5 points

STANDINGS:
Coco - 114 points
Bradley - 105 points
Benjamin - 98 points
Cody - 93 points
Hyson - 82 points
Jalen - 80 points
Deryk - 75 points
Aaron - 65 points
Yakov - 57 points
Terry - 50 points
Dheera - 2 points