Questions 1 & 2: Effectively, there is no file system. (Obviously, there is under the hood, but you shouldn't think of the phone as a file storage device as you do your PC or your current Android phone. WP7 supports Media Transfer Protocol, but not USB Mass Storage.) Without a file system, there's not much call for file management utilities. Also, the security model gives each app its own storage space. As such, even if one were to write an app to accept files over the network, those files would get stored in a place that only the server app could access, making them useless to other apps.
I tell potential buyers that if they want to be "users" of their phones, Windows Phone is great, but that if they want to be "administrators" of their phones, WP is probably NOT for them. Microsoft set out to make WP something between the wide-open chaos that Windows Mobile, Linux, or Android can be and the "walled garden" of iOS. They wanted something a park rather than a garden -- a bit more freedom to move around than Apple will give users but far less than Google will.
Question 3: When you connect your WP8 device to your PC via USB, you can see a "view" of the phone's files as presented by MTP. MTP exposes the music, videos, and pictures, as well as a "Documents" folder. You can drag files back and forth from/to the PC and the phone.
Question 4: WP8 runs one task at a time, with a few exceptions. Ignoring the exceptions for now, if a task is not visible on screen, it is NOT receiving any CPU time and thus not draining your battery at all. If you open an app then press the Windows key to get back to the start screen, open another app, and repeat, you'll have several apps loaded in to memory, but only the visible one is getting CPU attention. If the OS determines that it needs memory, it will unload apps as needed (probably based on least-recently used, but I don't recall for sure).
Q4 exceptions: Microsoft's first-party apps are allowed CPU time when off screen. These include the phone app, music player, and several others. Third-party apps have a few options for off-screen CPU as described below:
1) Apps may ask to keep running under the lock screen; this lets them keep working on tasks after the screen times out and turns off. It doesn't let the app run if you press the Windows key or switch to another app. This is useful for tasks that take a while to complete or that are by their nature long-term (GPS logging, for example).
2) Apps may use one of several functions written to allow background continuity such as VoIP calling, music streaming, and large data downloading.
3) Apps can register a "periodic task" and/or a "resource-intensive task" to get work done even when the app isn't running. (Think of this as a limited form of cron in a Linux world.) Periodic tasks are kicked off every 30 minutes and must complete within 15 (or 25, I don't recall) seconds, must not use too much memory (6MB?), and have no UI since they are run in the "background." (These tasks can display a toast alert or update a live tile, though.) Resource-intensive tasks get more time and memory (unlimited?), but can only run when the phone is plugged in (i.e., not on battery) and has a Wi-Fi connection (i.e., not cellular data).
4) (This one is only tangentially related to the multi-tasking question, but it's worth adding.) Apps can register for pushed data. A server can then push alerts and tiles to the phone whenever they want and as frequently as they want. Obviously, the information pushed has to be something that the server can know about since it is doing the pushing (via the Microsoft Push Notification Service). This means that server-initiated tile updates might not be a good idea for a weather app since the server won't know where you are at any time. (That's why most of the weather tiles use a periodic task to update their tiles. Our app uses server-push to let students know when new grades have been posted for their course since the source of the data is another of our servers rather than the phone itself.) Because this kind of background work requires a companion server app, few apps use it.