"He and I want a beer."
Translation:Él y yo queremos una cerveza.
Why can I not simply use "queremos una cerveza", the conjugation of the verb indicates that we all, including me would like a beer.
Rocko2012 is right. Imagin you were in a bar with four people more and you said: "queremos una cerveza", the waiter wouldn't know how many beers do you want, since he doesn't if this queremos refers to everybody or only to two of you, so he'd probably bring five beers. What you suggest would only be correct in my opinion if the only ones in the table were you and your male friend, so in this case "he and I" and "we" would mean the same.
You could but you have destroyed information. We know from the English it is two people and one of them is a male. From your Spanish we only know it is at least two people and we no longer know the gender of one of them.
I entered "El e yo quieremos una cerveza" and I got it wrong b/c it should have been "y yo"? I thought this software kept track of the lessons you've already done. I already covered y vs e.
You use "e" instead of "y" only when the first sound that comes after it is the same. In "y hija" for example the "h" is silent and the first sound in "hija" is the same as the word "y". So you change it to "e hija". Pronouncing two identical vowel sounds sounds terrible. "yo" doe not have that same vowel sound as the word "y" so it not a problem to say "y yo". And you only use "e" if it is needed.