There are many reasons it may not work.
Yes but it wont be in hd
go the internet exe and try to install sun java
No, but if you wont the HD quality and you wont to watch the T.V at the same time you will, otherwise you'll have to do without watching the T.V. But the HD PVR can record in SD as well.
Can a Elgato Game Capture HD work on a PC? I'm might get one for Christmas (getting the sims 4 and a pc) I don't want people to waste there money on something that wont work on my gaming system (pc)
An External HD is a hard drive that is in a separate enclosure other than your PC that connects via a wire. Most commonly USB, ESATA or firewire.
A printer, an external HD, pendrives.
iShowU HD Pro can record sound from external inputs/microphones.
You will be able to play it correctly, but it wont look as well as it would look on an HD TV
It could mean that the external HD is formatted with a file system that your OS can not access. If thisa is the case, either reformat the HD with an appropriate file system or install and boot to another Operating System (and maybe be unable to acess the files you already have on your computer)
Try running a free LIVECD and see if it will work that way. If it doesn't try a network install or swapping CD/DVD drives or use and external USB CD/DVD.
Simple answer: Yes.
If you wanted to watch HD DVDs on the 360 you would have to buy the extra external HD DVD player. This does not make much sense now because HD DVDs "lost" the format war to Blu Ray.