You'll get nowhere with this all-in-one PC, you won't be able to make it display on the TV. Well, you may, but it will be through several adapters and the quality will be terrible. Get an old PC tower and keep its frame, buy PC parts. Read about ArcadeVGA, soft15kHz and other 240p VGA solutions to know what's best for your needs. Forget about Windows 10 too, it's just not made for such a low resolution. There are Linux distributions tailored to what you want to do.
You'll get pixel perfect. As long as you are outputting 240 lines, your TV will display them fantastically. Just don't do something stupid like 1080p rendering downsampled to 240p. If by vertical support you mean pivoting the screen, you should be fine. Just tell MAME not to rotate them. If you want to play vertical games on your horizontal screen, then sorry but they will look ugly, if they look anything at all.
You'll get pixel perfect. As long as you are outputting 240 lines, your TV will display them fantastically. Just don't do something stupid like 1080p rendering downsampled to 240p. If by vertical support you mean pivoting the screen, you should be fine. Just tell MAME not to rotate them. If you want to play vertical games on your horizontal screen, then sorry but they will look ugly, if they look anything at all.