when I edit, after saving, white background appears around element

Actually, I can think of a few reasons you can have issues that sound like this. A couple that take more work to fix are if you don't save your PSD with the Layers box checked, or if you flatten the layers before saving. (Patching or content-aware fill can help fix those.

You can also get a white line around the layer if you have the Move tool selected, as it'll show layer boundaries of the selected layer, but that one will go away if you switch tools to use another tool. From your description, it sounds like you're just not familiar with that feature of Photoshop--it's good for showing you where the furthest-out pixels are so that in a file with 50 layers, you can tell for sure which element you're about to move or which layer you're about to paint on. Think of it like the Move tool's version of the Brush/Eraser outline to tell you what part of the layer/image you'll be affecting when you use the tool you've got selected.

Photoshop and PSE are a lot to learn at first, and sometimes confusing, but after you've used it for a while, you start to understand why the things that didn't make sense at first are actually super-useful for people who use it a lot. It takes time, though, so don't be too hard on yourself or get discouraged--every time it confuses you, it's an opportunity to learn something new about how to use it. Ask questions, lots of them if you need to...we all had to start somewhere, and most of us were lost the first few times we tried doing anything more complicated than opening a file in Photoshop. You'll be helping answer other peoples' questions in a few months if you stick with it, though!