As for reincarnation, there is no limit to what one can or will reincarnate into depending on what one believes.
Here's how I've understood reincarnation:
A) The basic tenet of reincarnation is that soul is on a journey to the Source or its Source. The dual desire of the soul is to both merge and/or seperate from the Source. Thus a major assumption and a logical one, is that it would take many lifetimes of experiences to exhaust all the desires to seperate from the Source.
B) A basic observation being made by reincarnation is the perceived discrepency or disparity, biologically, mentally and spiritually between people. Thus the assumption is that people have karmic dept from past lives.
There are many alternatives and possible explanations for all of this, but one commonality is we do live this current life with an ideal plan.
I guess your gender question is yes, one will logically be both during their many sojourns, if one is using reincarnation.