Quote: "How many -simultaneous- sprites can agk support in tier 1?"
There used to be a cap (10,000 I think) but I believe that has been lifted so your limitation is basically your device's memory. I highly doubt you'll hit the limit. Do remember that sprites are different to images. Images take up a lot more memory than sprites do.
Quote: " If I want to use my bought AppGameKit on a second PC, do I have to just uninstall from the first one?"
Check the licence. I don't have it on me right now so I can't check.
Quote: " Do I need a paid apple developer account in order to compile my code in my Apple devices "
Yes. For your apps to run on iOS Devices, they must be 'code signed' and to do this you need a code signing certificate from Apple, which you get when you join the iOS developer program. You can however, run your app on the iOS Simulators without having to have a paid iOS Dev account.
Quote: "- Has anyone succesfully delivered/ beta-tested an AppGameKit iOS game with the TestFlight service? "
Looks like it 
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