Taking the OP's questions in turn:
1) No, my DD is homeschooling, so I'm answering on the possibility that this may help you understand how homeschooling differs. It may not, because homeschool requirements vary. All of the information I have is specific to my state (LA).
2) If she said you can take a picture of art... can you also take a picture of the other subjects? You might try selling her on the idea that it's easier to send via email. Failing that, you could make copies. And failing that, you could try holding back some sheets, since I'm not sure you really want to keep everything forever anyway.
As for how that's handled in our program... the state does not require documentation until you want to renew your homeschool program for a new year, and since they do not want to be inundated with massive work folders from all corners, they require just a few samples from each subject area. The folder also has to include a list of all teaching materials used, and a simple outline of topics covered for each subject. Standardized test results are accepted in lieu of a folder, so that's one advantage you were expecting to find.
The bottom line, though, is that some form of physical evidence is going to be required, no matter what.
3) This is where your ISP option shows some value over ours, because in our homeschool program, curriculum is entirely up to the teacher. They do leave an option to borrow extra books from the local school, but the school can simply say no. Outside of the school, there are sets of curriculum available for purchase, but DW is basically developing her own, as she goes along, from whatever resources she comes across and approves.
The benefit is that DD gets a curriculum designed specifically for her. For example, whatever science topics they're doing, if it's something that captures DD's interest, they can go just as deep and broad as she likes. If it doesn't, they can do the minimum requirements and move on.
The downside is DW spends A LOT of her time on curriculum development.
Our program has no requirement for evidence of PE. That just sounds silly to me. My suggestion would be to check with the school for specifics on what qualifies as acceptable evidence. Will they accept a copy of the receipt when you pay the kung fu teacher? If they need something with a signature every time, you could make it easy on the kung fu teacher by putting together a simple sign-in sheet, fill in the dates, and then just ask the teacher to sign on the line each time. It may also be that they'll take your word for it, just not in verbal form... so a simple log, in which you record her activities, with date and time, would be an option.
