It's possible. You'd need to use Handbrake to do a batch encode of every video you want to sync, then drop those new files in iTunes.
I have 6TB of movies and TV Shows
1 - Yeah. My Mac Mini can transcode 1080p but the CPU usage is pretty much maxed.
2 - It takes 30 seconds on buffering before the video plays.
3 - You can specify the screen size (iPhone is 320 x 480), not tested it on iPad but I've heard good things.
4 - I've not tried this personally.
5 - I'll make another thread if we get 3 or more people. I can't imagine duty is much on $50 x 3.
Splendid many thanks EVH!
Put my name down for the dodo effort.