Kazan Chess

2. d4 ... b6/Be7

3. Bf3/Ne2/0-0/Re1 ... e6/Be7

4. Be3 ... Nf6/0-0/Qe8/Rd8

5. Nd2 ... d5/Rd7

6. e5 ... h6/Nh7/f6/Rf7/Qf8

7. Kf1/Ng1/Be2/Ndf3/Qd2/Rad1 ... fxe5/Bf6

8. Bxh6/Qe3/Rd2/Bd1/Qe2/Be3 exd4

9. Nxd4/Qf3/Nde2/Bd4/Qe3/Nf3/Nef3/Qe2/Be3

do you mean: 9.  ... Bxb2/Rf6/Rdf7 ?

if so 10 Nd4/f3/Qf2/Bd2/Red1/Ke1/Bf1/Qe2/Bf2/Qe3/Nge2

question 1: if you can remain in check until the last move of your turn, does this mean you can move into check so long as you get out of check before the end of your turn?

question 2: are you allowed to make a sequence of moves that results in the same position with your opponent to move?

the ansawer to question one will influence my next turn

Yes, the rules do not forbid it. Maybe by the end of this game we will have formulated rules that are better, but for now, there aren't really any restrictions.

11. Nxd4/Be2

1. e4/Be2 ... Nc6

 2. d4 ... b6/Be7

3. Bf3/Ne2/0-0/Re1 ... e6/Be7

4. Be3 ... Nf6/0-0/Qe8/Rd8

 5. Nd2 ... d5/Rd7

6. e5 ... h6/Nh7/f6/Rf7/Qf8

7. Kf1/Ng1/Be2/Ndf3/Qd2/Rad1 ... fxe5/Bf6

8. Bxh6/Qe3/Rd2/Bd1/Qe2/Be3 exd4 xd4 ... exd4

9. Nxd4/Qf3/Nde2/Bd4/Qe3/Nf3/Nef3/Qe2/Be3 ... Bxb2/Rf6/Rdf7 

10. Nd4/f3/Qf2/Bd2/Red1/Ke1/Bf1/Qe2/Bf2/Qe3/Nge2 ... BxN

11. Nxd4/Be2 ... Nxd4

12. Qxd4/Be3/Kf2/Re1/Rdd1/Qd2/Bd4/Qe3/Rd2/Red1/Ke1

1. e4/Be2 ... Nc6

 2. d4 ... b6/Be7

3. Bf3/Ne2/0-0/Re1 ... e6/Be7

4. Be3 ... Nf6/0-0/Qe8/Rd8

 5. Nd2 ... d5/Rd7

6. e5 ... h6/Nh7/f6/Rf7/Qf8

7. Kf1/Ng1/Be2/Ndf3/Qd2/Rad1 ... fxe5/Bf6

8. Bxh6/Qe3/Rd2/Bd1/Qe2/Be3 exd4 xd4 ... exd4

9. Nxd4/Qf3/Nde2/Bd4/Qe3/Nf3/Nef3/Qe2/Be3 ... Bxb2/Rf6/Rdf7 

10. Nd4/f3/Qf2/Bd2/Red1/Ke1/Bf1/Qe2/Bf2/Qe3/Nge2 ... BxN

11. Nxd4/Be2 ... Nxd4

12. Qxd4/Be3/Kf2/Re1/Rdd1/Qd2/Bd4/Qe3/Rd2/Red1/Ke1 ... Rf5

13. Bd3/Re2/Rdd2

Resigns.

new game?

I would not have resigned becuase the end game is much harder to win 

No I don't think I'm up for another game.