Maybe Remote Buddy, but with EventGhost, you have plugins to do more.
Honestly I don't use my example, I use a Harmony Hub instead. And there is a IFTTT action to run an activity (Step on Withings Scale in bedroom, Turns on TV). And since I use Kodi there are better was to automate things.
Yes, but you will need additional software. Apps such as Plex and Kodi have this functionality built in, but other apps would require you to use a tool such as Remote Buddy.
I would be very surprised if the thunderbolt connection doesn't do 1080p at a minimum. (But, I can't personally confirm.)
I don't have a remote recommendation for you either... BUT if you want to avoid buying a new remote, you can use the Plex iOS app as a remote for PHT. Also, RemoteBuddy is pretty powerful and allows you to repurpose all sorts of stuff you might already have lying around your house as a Plex remote (such as a wiimote or PS3 bluetooth media remote).
Check out “Remote Buddy” — I think it allows you to map Bluetooth devices to keyboard keys. Older versions work on PPC. I use it with a Wii controller on my G5