Well, I'm not sure I really understand all of this, but I notice the post keeps falling on the list, so I'll take a stab at it. Well, part of it anyway.
I've found that when I do a Web Gallery, it requires a "plan" before I ever open the Web Gallery screen. Maybe if I explain my workflow you'll find some clue to the problems you're having with yours.
I do all the editing for my images in PSD.
Next, I place copies of the pictures I want in the gallery in a new folder that I've got labeled something like "MtRainGalSource". (I never put all my pictures in a gallery, so you might be able to skip this step.)
Then I decide where I want my completed gallery to wind up on my hard drive after it's been created. I navigate to that location and create a new, empty, folder with a descriptive title like MtRainierGallery. Because I use a Mac, it's very easy for me to just set this folder up on my desktop so I know right where to find it quickly and easily. I don't ever use XP for creating these, so you'll have to figure out something workable for you on that OS. Just remember that it's your choice, so pick a place you'll remember!
So now I've got both my Source and Destination folders right where I want them. This is when I open the Web Photo Gallery option in Elements. From this point on, you just navigate to the location of the folder with your Source images and then navigate to the location of the folder for the "Destination". And, no, Elements doesn't know where you want this stuff - you've gotta tell it. (And if Elements ever does start doing this kind of thinking for me I'll have to find new software!)
After you've made your other choices in the Web Gallery set up area and hit OK (or whatever it is), the gallery will be created and the whole thing will land in that new folder you set up. Then it's up to you what you do with it next. It can either stay on your hard drive or be uploaded.
Elements won't be able to help you get any images off of your web site. Some other software got them up there, so some other software is going to have to get them back. All Elements does is create a folder of thumbnails and images that are READY for the web site.
Once you've created a Web Gallery, it is very awkward and confusing to edit, because if you remove an image, you've got to get both the thumbnail off the index page and remove the page for the corresponding larger image. When you remove something, you break the links. You know those little arrows that allow you to move backwards or forwards? Well, if you've got 10 images and you take out number 6, the forward arrow on number 5 won't know what to do anymore. The backward arrow on number 7 will be confused too, so all of those links have to be repaired. This isn't an insurmountable problem, but "trust me", you can create a whole new gallery in less time than it takes to do all of that "fixing"! I've been there and done that.
You also made reference to something you'd read about digging into the hard drive to edit. That might have been something I posted pretty recently when someone was asking how to change the fonts in a web gallery. To do that, you do need to access the templates within the Elements application folder. That doesn't have any relation to what it seems you need to do in this case. Any changes to a completed gallery have to be done within the folder that contains the web gallery pages.
I'm going to let somebody else tackle the problem with the quality of the images after they're posted. I have a couple of hunches, but this is getting too long for one post!