No, "האם" isn't necessary. You could say "?הן טובות" and by the inflection of your voice it would be a question not a statement. By adding "האם" you are making it more obviously a question. I'd say it's more common when speaking to leave the "האם" off. :)
Right. It's very often left off in speech. This is similar to English: "they're good?" can be substituted for "are they good?", except that in English it doesn't make it shorter. But you can leave it on. It won't make you sound pretentious.
In writing don't leave it off. It comes off as uneducated.