ElDiablo is right. Flash just doesn't perform well on PowerPCs. I have a 1GHz eMac with 1GB of RAM, and Flash games and videos are terribly slow. They;) work fine on my Intel MacBook however!
While connected to your TV, go to :
System Preferences -> Displays -> Arragement
Then drag the little grey bar from the MacBook Pro preview window to the TV preview window. This will make your TV the "Main" screen when you connect the MacBook to it.
Pressing Apple+Home and Apple+End will make the Home and End keys act like you expect. On the Mac, pressing just Home or End takes you to the top of the page, and the bottom of the page. (The keys were designed that way for reading, not editing.)
It seems to have something to do with the OS trying to draw a menu, or transparency. I recommend you install the machine with it's default load-out. (The software that came with the machine when purchased.) Then see if the problem still occurs. If it does, you can rule out software.
This is not an uncommon problem. The apple discussion boards are ful of people complaining about their MacBook powering off randomly. I keep meaning to take mine in to get it fixed, but there are great many people reporting that whatever Apple did to "fix" the problem didn't work, or caused...