I kind of wish you'd have spread these questions out over a couple of posts so that we could answer each thoroughly. If I answer all of them in depth in a single post, this answer would be the size of one of my books! (which, by the way, contain many of the answers to these questions.)
1. The default save location for your videos should be the last place you've saved your video to. So that should happen automatically. Although in my books I recommend that, whenever you start a new project, you create a new folder for it. This is good housekeeping and a good way to keep your tmp and render files in the same place on your drive, which has a number of advantages.
2. You can't create a custom project preset. The only presets available are the ones Adobe provides. And, although they are pretty extensive, some non-traditional formats (like video from some mobile phones) are not well supported. You may be able to get it to work -- but it's usually a hybrid solution and, personally, if you plan to use your phone's video as your main video source, I'd recommend you look at another video editing program. Premiere Elements doesn't do the hybrid stuff well. It's ideally suited for video from traditional camcorders.
3. The thumbnails you see when the program loads are not in your current project. At least not until you import them into your Project panel. That Media panel is merely a preview to what's in your Organizer catalog. As I explain in my book, it's usually best to ignore this panel until you really learn your way around the basics of this program. It's very confusing. Fortunately, it adds very little load time to the program itself -- regardless of how much time it seems to add.
4. The thing in the illustration is the Work Area Bar. It's used to isolate a segment of your timeline for rendering, etc. Usually, it will shrink and grow as you add and remove video from your timeline. Unfortunately, there's a bug in version 9 and, if you manually change it once during a project, you'll have to manually change it for the rest of the time you work on the project. But, if you drag each end of the Work Area Bar to cover your entire timeline of videos, your project shouldn't misbehave.
5. The "gap of nothingness" on your timeline is just room for you to add more audio and video tracks if you'd like to. It's a good thing to have! BTW, as I'm sure you know (and my books, once again, explain) you can toggle the tracks on your timeline so that they display as either compressed (as in your illustration) or wide open, which allows you to see your clips and control audio and video levels. Once again, this is a very good thing!
I've horked something on my computer then. I edit a video, click on share, change the destination folder and create the new video. I exit and I save my project, closing Premiere entirely. I re-open Premiere and re-open my project. It successfully remembers the last video I was working on, but when I go to share the video it is back to the default Documents folder, not the folder I saved the video to. It remembers while I have Premiere open, but never does when I exit, no matter how many times I save the project.
It's not a big deal, it's just annoying. Like if you give your video a name, then change the preset, Premiere switches the name back to Untitled. I've just gotten in the habit of putting the file name on the clipboard so when Premiere decides to change to Untitled, I just paste it back in.
Meh. None of this is really make or break, it's just minor annoyances.
It does this for me as well no matter how many times I change the folder