Why mädchen ein not eine
(das) Mädchen is neuter, not feminine. The reason is that it's a diminutive (you can look this up), and all diminutives are neuter in German.
What is the diminutives?
Anything ending in -chen or -lein is a diminutive form, and generally means a smaller or younger version of the root word.
What if the sentence goes like, a child and a girl. Would it be correct to say it as, ein kind und ein mädchen?
yes, since Ein is the same for both masculine (Ein Mann) and neuter (Mädchen, Kind)
I wrote ¨A girl and a women¨Why is this wrong?
It should be 'a woman' women is plural