Games played per week

Question
If the coach has a player play more than the games she is allowed per week can the player be suspended any games for this even though the coach told her too?

Answer
I will speak to this generally as the participation rules may vary by state.  Typically, if you use an ineligible player in a contest, when the violation is discovered that contest is forfeited.

A play can be suspended by administration or the coach.  Suspension in this situation seems a bit unusual, other than she shouldn't play in any games until she becomes eligible again.

The bigger problem in your picture is the coach.  Any coach that flaunts the rules like you describe is demonstrating text book unsportsmanlike conduct and should be replaced.  I say this only if the coach was aware that what they were doing was wrong.  If it was unintentional, then the forfeit of any games won, that this girl played in, while she was not eligible is proper punishment for the team.