Opening mistakes

In one of my blitz game in playchess (in which I` played ar white) started in following way 1.e4 c5 2.c3 d5 3.exd5 Qxd5 4.d4 e5 5.Nf3 and there my opponent made decisive mistake 5....e4?? and after 6.Ne5 with threat Bc4 white won easily.

In one 15 min OTB game played in this evening (I` played as white in this game too) after 1. Nf3 Nf6 2. d4 e6 3. c4 b6 4. e3 Bb7 5.
Bd3 c5 6. O-O d5 7. cxd5 my opponent mistaked 7.....Nxd5? ( the best for black was7... exd5) 8. e4 Nb4? (other mistake - only way to avoid losing was 8....Nc7 but anyway after sacrificing pawn 9.d5, white gets dangerous initiative) 9. Bb5+! Bc6 10. Bxc6+ N4xc6 11. d5 with almost decisive advatnage and black found nothing better than to give up pawn with 11...Nd4.