Once you buy an App it can be downloaded from any device using the same account without additional charges. To transfer data, you'll need to root and use a backup app, like titanium backup or my backup pro.
I'm not sure if this will work, but, one time, I pulled app data off my phone using my PC. Then, later, I put it back on and all of my save data was there. Not sure if this will work going to a different device, but, it couldn't hurt to try and install an app on the tab, and, copy over any related data from your phone, to see if you can get your saves.
Sorry, don't have a tablet, so, no opinion for your bonus question.
I don't have an android device yet, so I'm not sure how much access you have through file manager. I use a free dropbox account to send app data save files to and retrieve from between my iPad and iPhone.
Actually there is a jailbreak app for ios that does this (for app save data and settings only)by clicking the apps name in a list and hitting backup or restore after syncing with your Dropbox account. All the file management is done in the background for you. Quite nice. Dev idea for android if it's not been done yet?