General Help with replacing shut off valve under kitchen sink- Pics included?

Hi guys, my parents had me install a new faucet in their kitchen sink. It works great and everything, but after the install the hot water pressure basically decreased greatly. The cold water pressure is fine, but I believe after I had turned off the hot water at the shutoff valve, something in the valve got messed up and is blocking the water supply. After turning the hot water valve off and on repeatedly to see if there was a difference, at times I would get really good hot water pressure, and other times I would not, all when opened completely. So something in valve is screwed up I believe. Now, no matter what I do, whether I open the valve all the way or I close it all the way, the hot water pressure is identical and remains low (meaning water even comes out now when the valve is closed). I cleaned out the brand new faucet's aerator after doing this and got a bunch of black junk, so something was breaking up in the valve (mineral deposits, maybe gaskets, etc).

Bottom line, I need to replace the valve, which I have never done before. I have included pictures below to show you my set up. Sorry for the poor lighting and photo quality, the pics were taken on my phone's camera.

My questions are, what kind of valve is on my copper piping? I have seen people unscrew other shut off valves online, and sometimes people cut the copper pipe. I would rather unscrew this one but it seems like there are no nuts on it. The top nut in the photo is from the new faucet line, and the bottom has no nut. So the big question I have is can I uncrew this valve and take it off my piping without cutting the copper pipe?

I would rather unscrew it and then install a new compression fitting, but it seems like there are no nuts to unscrew. Also, any suggestions on what valve size or type I need?

As you can tell, this is a very basic job but I have a lot of questions since I have very little plumbing experience besides solvent welding pvc together.

Thanks for all the help

Here are the pics:

http://cdn.plumbingforums.com/forum/attachments/f2/2386d1333388397-general-help-replacing-shut-off-valve-under-kitchen-sink-pics-included-img_20120311_222347.jpg

http://cdn.plumbingforums.com/forum/attachments/f2/2387d1333388397-general-help-replacing-shut-off-valve-under-kitchen-sink-pics-included-img_20120311_222406.jpg

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