Моя is for feminine nouns and мой is for masculine nouns.

Exactly what I wrote!

That should be correct, but it translates to we are with mom, and they wanted my mother and i..

This is how I learned to say it in Russian 101 in college!

According to this site I found on the wondrous glory that is Google,

You need to use а in cases when you wish to switch your attention from one event or fact to another (1) or to stress that two events contrast in some way. That is, one of the circumstances (3) or the whole situation of the second phrase (2) contradicts to the first event. For example:

1) Я слушаю новости по телевизору, а он читает их в Интернете. I listen to the news on the TV, but he reads online newspapers. 2) Я знаю ответ, а ты -- нет. I know the answer and you don't. 3) Мама уехала на дачу, а папа -- на рыбалку. My mom went to dacha, while my dad went fishing.

On the other hand, you would use и to stress the temporal (ex. 1 below) or causal (ex. 2 below) relations between the two events, or to say that the two events both support the same idea (ex. 3 below):

1) Я слушаю новости по телевизору и потом проверяю их в Интернете. I listen to the news on the TV and then compare them with the online newspapers. 2) Я списал ответы у Паши и сдал экзамен. I copied the answers from Pasha and passed the exam. 3) Мама уехала на дачу, и папы тоже нет дома. My mom went to dacha, and my dad is not at home either.

And for future reference, the difference between но and а is that но is more for contrasts (I speak poor English, but I understand it fine) while а is more for clarifications (That is not a raven, but an apple).

I also put a instead of и.

а vs. с vs. и? Anybody?

https://www.duolingo.com/comment/11915869

"Моя мама а я" sounds like a title of an essay which contrasts the author with their mother.

Yes, because а is but, so the translation would be my mother but i

You could say this, but they wanted my mother and i rather than i and my mother

Because it specifically says "MY mother and I." You need the "my."

I agree it should be. <<моя>> is implied by the familiar use of <<мать>>

"а" most often means "but" but "и" pretty much always means "and".

In terms of trial and error, the Duolingo site includes more information about grammar, but you're right- there's no way i would want to learn a language from scratch using the app.

For example, you could write "дерево зеленое а небо синее" - in English this means either "the tree is green but the sky is blue" or "the tree is green and the sky is blue" - here the conjunction literally means two different things, but in the context of the sentence it means only one thing.