So many things to respond to 
Installing .APK’s outside of the store:
This is called “Side Loading”. Every Android device except for the Nook should let you do this. However it is disabled by default on many devices like the Kindle Fire. You have to go into the settings and enable loading from unknown sources.
I would hope that people would be more trustworthy downloading an app directly from the creator’s site, as long as I felt that creator was trustworthy and not writing some malware. Downloading your app from some other person’s site should be a red-flag. Please note, if you do this, any one can copy your app and distribute it too.
Nook and Amazon have pretty thorough review processes similar to Apples. Google Play does not. Therefore garbage apps will get uploaded to Google Play and it doesn’t help its reputation.
Also most people who get apps from Google Play expect them to be free.
As for hardware issues… welcome to the wild wild west of software development. If you’ve ever tried to wrote apps for Windows, in particular anything that wants to use hardware, you will know the drama that Google created when they built an OS that’s been pushed to a 1000 different devices by dozens of hardware makers and no controls. It makes building for and supporting Android a pure nightmare and may be worse than building for Windows.
The good news is that unless you’re doing weird hardware stuff, just a straight up game it should run pretty well on any armv7 hardware running Android 2.2 or later. Except the Kindle Fire which apparently doesn’t support custom fonts.
Now the really good news is that both the Amazon and Nook markets actually have people who buy apps and you’re for the most part targeting a limited set of hardware.
Finally as far as the 7" form factor being preferred, after having the Kindle Fire and having played with the iPad, I would have to disagree.
Weight wise the new iPad clocks in at 23 oz. The smaller Fire is almost 15 oz. Given the size difference the KF is a heavy bugger. Its too big to grip side to side, but its too small to use it in a lap, or on a stand. I find using it very awkward. In other words you pretty much have to 1-hand it all the time. The iPad and other 10" models you are only 1-handing some of the time.
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