Hi, here are some references taken from *Algebraic geometry I. Schemes.* by Gortz and Wedhorn, Appendix E.  These are generally scattered in EGAIV as far as I remember.

**EDIT:** I originally misread what Gortz and Wedhorn were saying, and got the references wrong.  Here are corrected references:

1).  This is Appendix E.1(11).  They reference EGAIV, 12.2.1

2).  I don't see this in their list...  You could try checking out EGA.

3).  Normality is Appendix E.1(20).  They reference EGAIV 12.2.4.  Smoothness is Appendix E.1(18), again see EGAIV 12.2.4.

Of course, they are talking about geometric normality etc, but in your case, the residue field at the special point is $\mathbb{C}$, so if its normal it is geoemtrically normal.

In particular, they state the openness of the statements for a proper flat map.