Okay, first... that's right on about the 800dpi setting... it's only for vectors. I was being stupid again I guess.
Saving swatches - they are document dependant as was noted. You can make your own libraries that will show up in the library picker by making a blank document, saving some swatches and saving it as an AI file in the libraries folder in your Illustrator program folder. "global" color refers to how a process color is linked within a document, not whether it's carried over into other documents. There really isn't any way to permanently have a swatch library active like you do in Photoshop.
Eyedropper - make sure you aren't trying to eyedropper a raster graphic, it doesn't work. The eyedropper tool in Illustrator isn't for sampling screen colors like it is in photoshop. It samples attributes of objects. Double click the eyedropper tool in your tool box to see all of the things that it will sample (or "copy" if you like).
Layers don't work exactly like they do in photoshop. Don't think like you're in photoshop, it will just confuse you. You really have to attack Illustrator on it's own terms. They really work more like photoshop's layer sets if you must make a comparison.
The "freehand pen tool" in photoshop is similar to the "pencil" tool in Illustrator.
The only things I can think of is that you are turning off the layer's editability when you leave for some reason, or you are using the wrong tools to access the shape. You need to switch to one of your selection tools to regain control of a path that's been built already. So if you create a shape and then start working on a new shape or layer or whatever and the shape deselects... to start working on the previous shape, change to something like the direct selection tool or the path selection tool (the white or black arrow in the upper left of the tool box where the "move" tool would be in photoshop") and grab or marquee select the shape to make the anchor points and paths show up again.
Lastly, the best way to deal with Illustrator is to think of everything you make as it's own little object. Each object has it's own attributes that you can edit. There are some confusing ways to address this unfortunatley that hopefully Adobe will address in 11
. If you are trying to edit the color of a stroke or fill and it just won't change, try checking the "appearance" palatte to see if there are multiple strokes or fills applied to the object. It's confusing that these settings can override eachother, but it's easily overcome if you are aware of it. IMHO this is programmed poorly. One of the few things in Illustrator that's just bad. They should just move entirely over to the appearance menu and they'd be okay. But for now, it's confusing.
Hope that helps.