2. Is a 7" or 8" tablet big enough on Android? The 9.X screen on the ipad I played with seemed just about right. Not sure if going down to an 8" would be really bad, or just a tiny step down.
That should be plenty. It looks great on my (admittedly very large-screened) phone, and it looks pretty good on 7-inch and 8-inch tablet screens as well. I actually prefer the way it looks on slightly smaller screens (I think it looks better on a 7" screen than a 10" screen personally).
3. Hardware recommendations. I've read a thread or two about incompatible android hardware. I've found some deals on a few tablets and would like opinions:
A. Samsung Nexus 7, 2012 model
B. Samsung Galaxy Note 8 . I think that's what it is, as it's an 8" and the vendor was calling it a "Note".
C. Samsung Galaxy Tab 3.
The "Note" in Samsung land just means it comes with an integrated stylus that communicates with the tablet (i.e. you can see where it will land before it does, and it has a button that can be programmed and other neat tricks). The Note line also generally have nicer hardware than the Tab line (the note has a better processor as between those two), and the Note in your lineup also has slightly better guts (and IMO a nicer screen) than the 2012 Nexus 7.
My wife has the 2014 version of that Note tablet and she absolutely loves it. I have the Note phone exactly because of the high-quality stylus (almost no other devices on the market have a stylus that works as well). JRemote looks great on both, but I actually prefer it on the phone myself.
So I would almost certainly recommend the Note if it weren't for the fact that it ships with Android jellybean (4.1), but the nexus ships with the same version, and the Tab is only at 4.2.
4.1 is the minimum version for compatibility with JRemote right now, so buying in or near the minimum spec is a little risky. It should work, but who knows what will happen in the future. But just because the tablets ship with 4.1 doesn't mean that they won't get one or two version upgrades. You might want to research whether samsung/google are offering OS upgrades for those models before you make a decision (for example, I've seen conflicting discussion about whether the 2013 Note 8 got 4.4 or not). That said, you can always root them and do your own upgrades to Cyanogen Mod or whatever, if you're comfortable voiding your warranty. I'm running JRemote on CM 12/Lollipop on a little development board I've got (an exynos 4412, a close cousing of the chip in those samsung tablets) and it works pretty well.
I can't comment on differences between ios and android though as I've not used the ios version.