"It's hailing!" would be more natural English (accepted).
Either one could be used, but it depends on the situation. For example, when talking about a climate, you could say, "It never snows here, but it hails!"
Yes, but as an isolated sentence "Het hagelt!" is much more likely to be "It is hailing!" (like "It is snowing" later in the lesson).
You're allowed to translate it like that if you want. Either one is totally fine.
What Howard is saying is that it is not fine to say "it hails" which I totally agree with (native English speaker) it is both archaic and has a different meaning in English.
"it hails" on it's own means 'it calls' like it's calling a taxi.
If you don't want to say "hailing" the only way to say it is "it is hail"
I understand what he's saying and that's true that it would be uncommon, but either is grammatically correct even if you wouldn't use one of them 99% of the time. If you're talking about the weather in general and not at a specific moment in time, hails would be grammatically correct.
I said "It is hailing!" is "much more likely." "It hails" is certainly possible in certain contexts. ("it is hail" is possible if "hail" is a noun.)
Oxford dictionaries seems to suggest otherwise:http://www.oxforddictionaries.com/definition/english/hail
1 (it hails, it is hailing, etc.) Hail falls"