However, the problem you are going to run into is that Core2Quads run on LGA775 and Core i5's run on 1155. That means that an i5 chip physically won't fit into the same motherboard as your Core2Quad. Basically, to get yourself a new CPU you are going to have to build a completely new PC.
It sucks but that's the way the world is. I do feel your pain. I'm stuck on a Q8200 and can't quite get the cash up to do a full system update yet.
The Core i5 is faster than the older Core 2 Quad. If clocked at the same speed the improvement would be on average 20% - 22% more processing power. There aren't any AMD CPUs that can stand up to a Core i5 CPU.
Of course you will need to buy a Socket 1155 motherboard for a Sandy Bridge Core i5 CPU.
if your case is atx compliant yes, or can take a matx board. Have you got a friendly shop nearby that you can take it to?
To be honest there's not much of a bump from Q6600 to I5 in the real world, what do you use it for?
In all likely hood you won't be able to upgrade your Dell to a new CPU/Motherboard. The vast majority of Dell machines are what's called BTX form factor which basically means the motherboard is mounted on the opposite side of the case and upside down when compared to normal ATX machines (effectively a mirror image). This means ATX and BTX boards cannot be swapped. The notable exception to this is Dell's XPS line of PC's from a couple years back which used "Dell-ized" ATX boards and can be easily upgraded (XPS 630i and 730 come to mind off hand).
At any rate, as already noted you won't see much of a real world improvment moving to an i5 and you'd be much better off spending some money on a Solid State Drive (SSD) and performing a clean OS install.
Actually that is true. Many times a clean install of Windows will speed up a sluggish PC because the Windows Registry can grow larger over time installing and uninstalling programs. Grow too large and it can slow down your PC a little bit, worse, if it becomes corrupted, then it can make your system unstable.