1. Android runs on both tablets and phones. There is much difference other than some apps can be designed to take advantage of larger screen an provide a more tablet like experience. I've noticed that 7 inch tablets however get a phone style layout for apps, which I dislike.
2. Most apps will run on most versions of Android. Though there are a small number of apps that may require Android 4.0 or later for example to work. But for the most part the advantages of having later versions of Android are new features and performance improvements in the OS itself. Android 4.0 has a nicer UI, 4.1 has a performance increase to the UI, 4.2 unifies look of the UI between tablets and phones (buttons and system bar were in difference places before).
3. Android 2.3 can probably run most Android software, but some software may require newer version. Chrome browser for example only works with 4.0 or later.
4. Not sure, but I would believe it should be able to do that.
5. Android gets updates from the hardware manufactures, with the exception of Nexus devices that get updates directly from Google. End users are pretty much stuck waiting for the manufactures to push updates to their device. Unfortunately most devices get 1, maybe 2 updates if they are really lucky. Nexus devices are pretty nice because they get updates faster from Google and get more updates.
The exception is if you are particularly geeky type of person and can unlock the bootloader of the device you can install a custom ROM developed by a far superior geeky person. These ROMs include customized versions is a way to get a newer version of Android on a device.
6. Google Play is the primary application store for Android. There are over 700,000 apps in this store. The store also provides easy updates to apps. The store also provides access to other Google content like movies, books, and music. Most Android tablets have Google Play. Tablets that don't usually have an alternative store with will have far fewer apps. Amazon Kindle tablets for example don't have Google Play, but using Amazon Appstore, which is a sad alternative because if the much smaller app selection.
It is possible to install Google Play on many tablets that don't include it. Though it can be tricky on some tablets.
7. Not exactly sure what you mean, but I suspect you are asking with the difference is between the stock UI and third party UI perhaps? The stock Android UI is pretty light an minimalist. I provides usually most the features people need and runs smoothly. Hardware manufactures like to differientiate their devices with custom UIs that add more features and a brighter appearance. Though the new features often sacrifice some performance and use up more space in the internal memory and storage.