I use the Armorlite case. I got it the day after I bought my DS Lite and I'm loving it. However, there is one problem I have with it.

It may just be me, but when I have it on, it looks like the top of my DS Lite is smudged. I've taken it off several times, wiped them both down, and put it back on, but the smudges appear there again. Keep in mind, there's no damage to the DS Lite or the Armorlite. It just looks sort of bad with the smudge.

I still recommend it VERY highly, ESPECIALLY if you don't carry it in a case like me. I don't feel at all nervous sticking my DS Lite in my pocket or in my backpack with this on.

Yes, Sony has fixed the newer PSPs being produced with raised D-Pads and buttons.  Since you like playing fighting games, it doesn't seem like you have much choice but to trade it in for a newer one.

However, there are attachments you can put on top of your D-pad to help with that problem, but they're usually an eye-sore.  You can probably find them on eBay or something. 

From the sound of it, either the thumbpad or the place where the thumbpad connects to is worn down. You could get replacement nubs, but if it's the place where it connects to that's worn down, it won't help.

Your best bet could be just gluing it back on. That way, it doesn't matter which part's worn down because the glue's going to hold it in place.

I'm also having alot of trouble hitting those diagonals.  As far as making it easier..  I remember there being an attachment you can stick on your D-pad to help with that.

 I've also heard that the newer PSPs that've been manufactured also had raised D-pads for easier diagonals.  There's also a mod that involves opening your PSP to stick a piece of paper under the D-pad to raise it that way.  That'll void your warranty though.

 Myself, I'm planning on trying the mod.  I have a launch-day PSP and since the warranty's been long expired, I'd have nothing to lose.

Haha, I try twisting the PSP in frustration everytime I get my butt handed to me in Tekken 5: DR.  Freaking cheap computers.

Anyways, my PSP does get pretty greasy after a good hour or two of gaming.  I just wash my hands, wipe it down, and start all over again.