"He and I want a beer."
Translation:Él y yo queremos una cerveza.
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 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.