Not sure when this is due (if it hasn't been completed already), but I'll take a shot at these.
1. Do you find value in being able to fish a variety of water?
Yes, although here there is basically either freshwater or salt water. The freshwater tends to be either cold and semi-clear up farther north where I don't go a lot, or very murky, dirty, and warm like it is where I live along the gulf coast. Different waters definitely offer different opportunities to catch different species of fish. For example, river/brown and rainbow trout up north, whereas down where I am we have flounder, snook, red fish, black drum, crappie, and several species of bass, including striped.
2. Would you pay money to fish private ponds that are more convenient and/or offer better fishing than what you currently fish?
Possibly... but I'd want some kind of guide service or boat access (rental or whatever) that came with it if it was a larger body of water. I'm not really familiar with this concept though, most people here would allow you to fish their ponds without any kind of fee cause that's how we country Texas people typically are. The one stipulation there would be to require some sort of imposed size limits on keepers. For example, in my own catfish/perch pond there is a certain size of female I will not take for eating because they are my mother fish and I want them to continue to spawn for the next years.
3. If so, how much would you be willing to pay per day, week, or season to fish this water?
Again, I've never actually done this so I am not sure what's fair. But let's say it's a lake that includes a guide and/or boat access for the trip. I could see $100-125 / year for something like that. Think there is actually a lake near me that does offer such services for around that price. Personally, I cannot budget something like that but a lot of people do.
4. Would you use this website/app? Why or why not?
The idea is intriguing, but there are a lot of sites already out there for similar reasons. My one thought of that is that the site would need to fresh, laid out cleanly, and have frequent updates to make it worthwhile. For instance, Fishify is an app used by a lot of people, but it's rarely updated in my area. The fish reports are few and far between and not very recent, dating back to a year or more.