I think it's perfectly reasonable for you to have to follow up with them in terms of focus, etc.; a person-to-person chat will get you a better idea.
And they may not realize exactly how much guidance, or even information, you want/need.
And they may also think that you are capable of researching your own info about the event, etc. And getting a press pass from the planners if the event isn't free. All by your ownself.
They may expect you to be like a photojournalist, and scope out the barbecue, looking for events that are photogenic and that tell the story of the event (big crowd around the dunking booth? pics of that! Nobody doing anything interesting at the ring toss? pass on those pics).
They may be expecting quite a bit more initiative than you are delivering. If this is a day job for you, or even a frequent hobby, I would expect you to do those things, if I were them. And if I were you, I'd do those things.
I'd expect to be given the NAMES of the restaurants, but I would be capable of calling the owner or manager and setting up and appointment. And I wouldn't need a shot list.
If I were asked to take pics at a local restaurant and had been given no guidance, I'd take shots of the exterior, shots of the interior, shots of the host/chef/owner, shots of the kitchen, shots of a table w/ food, and maybe closeups of a dish or two. If I could get the menu items the reporter was interested in, I'd like that, but if I didn't have it, I'd ask them to prepare the specialty of the house.
Of course, that could be a lot of wasted film (bytes?), and time--so I would expect to have a *conversation* with the writer. In which I would expect to guide them: "How much room for photos do you expect to have? Is the article written yet? Or in the notes so far, is there anything special about the restaurant(s) that I could try and get a pic of? How much "food porn" do you want, or would you rather focus on people, or places?"
But if I were the writer, I would be hesitant to give you a very detailed list, because I'd be afraid you'd go out the take a pic of the exterior and interior, but not of food or people, or the pretty table settings, because "that's what you told me you wanted." I'd *want* you to exercise your artistic eye in CHOOSING what to photograph. Not JUST do the technical aspect of taking a well-exposed photo.
And if what's missing is basic stuff, thn you might create a fresh form for every story and email it back to them, asking all the questions in an easy "fill in the blank" format. That might work.
(I think the writers are expecting you to check that they're filled out properly)
As for #3--I think you have all the info you need. Loop the intern in, if only so she can see how the workflow and communication go. If it were *important* for you to give the intern assignments, someone should have told you that. But hey--if you WANTED to give the intern an assignment, since you asked, I guess you can. I'm not sure what more you want from that.