A) Yes there is, and a big one : 16:10 "TV" are not HDTV, they are monitors in disguise, which make VERY POOR TV. That's because in the best case, they have very poor logic for everything TV related. For console gaming, it makes a huge difference. Those TV are all very bad.
Every good HDTV is at least 16:9. 16:10 being mainly monitors, they are only good for PC gaming.
So don't be fooled, and avoid 16:10 so-called TV if you want a HDTV.
B) Yes it's true, you can take your calculator and find out for yourself, and no, they're no HDTV, they're monitors in disguise, which make very poor HDTV. One of the thing that make them so poor, is that they have to scale the image by a non integer number. Scaling correctly by an integer is hard enough, but with these resolutions, it will be very poor.
C) 720p/1080i/1080p doesn't mean anything as long as you don't know what they're talking about. There are two very different things that can be called that: what signals the TV will accept, and what the TV actually displays. "Scaling from 16:9 to 16:10" is pure BS, there is no scaling to have, as it won't fit more than 16:9, and if they did that, it couldn't look perfect at all. Avoid these at all costs.
What you cited shows a confused consumer that don't understand what he bought, and who believes that because his TV shows 1080p (which is the signal the TV received) in a corner, it's displaying all the 1080p signal (it doesn't if it's a 720p TV, it downscales the signal, so lose A LOT of information).
D) There's no TV that currently has 1920x1080 pixels below 26" anyway, as that's hard to do, and yes, there's no point. I saw they sell 1920x1080 monitors at 26", but I didn't verify if it was true. Anyway, there's no point in making or buying a 1080p TV below 40", that's why even SXRD TV, which uses 3 small 1920x1080 matrices the size of a thumb, actually start at 50", while they could make even 10" TV. So no, there's no difference.
E) Yes, the difference is huge, especially for consoles like the Wii. You'll see some people complain that the Wii is no 1:1 because they see lag in the controller, when in fact that's their TV that's too slow.
You also have to understand that the response times TV makers give you, are without any treatment applied to the image. The logic applied to the image by every TV adds several ms to your response time depending on the technology. The game mode of some TV actually removes lots of logic, sometimes downgrading the image a lot.
F) 16:9, true 720p in your case, as you have a limited budget. That means a 1280x720 TV. Not ever the worst HDTV, which are the LCD at 1366x768. You can tell these are the worst TV, as most people who have them complain that SD content (like the Wii) looks very bad on them. I've yet to understand how people can buy defective TV that can't at least display old content as good as SDTV, but it seems these are those that sell the most, making the most money to TV makers, as they're the poorest TV, so need less engineering. Don't be fooled, SD content on your future HDTV should look at least as good as on a SDTV.
G) 26" HDTV. There's no way the 19" can show 1080p anyway.
H) NoI) You can find cheap HDMI cables on the Internet. Cheap noname cables are OK, as long as you don't need more than 3 m (10 ft?) cables.
