Does a person choose their parents?
A person will assess and evaluate the life experience they need and then start planning their incarnation on the physical plane. They will determine what the priorities are to experience and then evaluate which options on the physical plane will most likely provide those opportunities and experiences.
The person who desires to enter the physical body may choose a body that has predisposed physical traits and in certain social or societal features that will help that fragment to obtain the life experience it desires. But physical abilities for a large part are determined by the gene pool of its parents and social and economic ability are determined by the society. Therefore, if a person has a talent of physical ability to perform or learn or do something on the physical level, this comes from the physical body. The obvious example of this is physical strength, but other talents are also developed through this manner.
Does a person choose their gender?
A person will choose the gender they want in a lifetime experience. Everyone has experiences in being a male as well as a female. Often the female gender is selected when a fragment wants a more spiritual growth experience. This is usually because the female gender is usually the more spiritual and sensitive of the genders.