The dual core is definitely faster. What do you use the computer for? What operating system will have it have and how much memory?
Everything should be ok but will be slow when converting videos. You might want to think about getting one with a quad core processor in it.
A video card won't help with converting videos. Converting requires cpu and ram.
It will cut the time down, yes. But the Core2 series is outdated these days, so it will still take a while.
It will be faster, no doubt. But I can't give you a specific time.
Higher numbers means higher performance. However, each processor has a specific model (E5500, E4300, etc.) so you'd need to know the specific CPU you're gonna get. If it's the one you ranked above, it's more than 4 times more powerful than your P4.
I too was thinking about a refurbished computer but then got to thinking about what if the system, specifically the hard drive, crashed. I don't think they supply you with the Operating System and motherboard drivers on separate disks, its all on the installed hard drive.