Why is "la senora" wrong?
The would be "the lady" in English, which is not the same as "the woman".
I am assuming my "la dama" is even worse. :)
how do we know when to change the word come to comen or comes and such?
Use "come" for 3rd person singular (él/ella come, that is, he/she eats) and "comen" for the same in plural (ellos comen, that is, they eat). Note however that the formal "you" (usted/ustedes) use these forms as well: usted come / ustedes comen.
I forgot the other persons: yo como / tú comes / nosotros comemos / vosotros coméis. That is, I / you / we / you eat.
should it be la mujer comelo
nope. "The woman eats it" would be "La mujer lo come." You can only attach object pronouns to the end of infinitives or participles, not conjugated verbs.
Why can't it be "Las mujer"? Why is only "La" acceptable?
Las will be plural. Las mujeres
Why wouldn't I use el arroz here instead of just arroz?
Because if you used el arroz, the sentence would be "the women eats the rice".
why is comen wrong?
It's not wrong. But maybe you used it in the wrong person ("él come" vs. "ellos comen")
Why is como wrong :(
como means "I eat" (first person singular).