If the male symbol is an arrow and the female symbol is a cross, then can the male symbol point downwards instead of up towards the right? Or would that make it a female symbol?

Actullay these symbols are two standard gender symbols, which is denoting male ♂ and female ♀ and are derived from astrological symbols. In any case this cannot be changed as it denotes the classical planets Mars and Venus. These symbols have been in use since the Renaissance.