I wrote a tutorial for exactly this situation. So this should help you quite a bit.
https://forum.inkscapecommunity.com/index.php?action=articles;sa=view;article=47For your question about selecting, it sounds like it's time for you to discover the status bar. Whenever you are using the Selection tool
, the status bar will identify whatever is selected. So in your screenshot #4, you can see that the status bar say "Group....". Since you've traced everything yourself, apparently at some point, you grouped some things. If you had downloaded the file from somewhere, or converted it from another format, groups are automatically created. But in this case, it sounds like you must have done it yourself, but forgot? (Or possibly you were just experimenting.)
So all you need to do for that problem is Ungroup. You might have to ungroup more than once. But just watch the status bar. When it says "Path...." then you're down to the basic path and rid of the groups.
For the problem identified in image 5, it looks like you're using the Paint Bucket tool, to fill with color, rather than a traditional fill. I would suggest not to use the Paint Bucket tool. Not using it will require you to have a separate closed path for each object. So there will be extra work. But you will have a better file in the end.
The reason when you pull away the black line, and the color stays behind, is because of how the Paint Bucket tool works. It creates a brand new path to hold the color. This tool has good uses, but only once you understand what's happening, can you decide if that's best for your project. If you're drawing (tracing) the paths yourself, you might as well create duplicates of the paths which are shared by adjacent objects, so you can have a separate closed path for each one. Then they can be filled with a traditional fill.
I would suggest not to use the SpiroSpline mode for a map. It's specifically for creating fancy smooth curves. If you want the map to have curves rather than strict boundaries, that's fine. But it's bound to be confusing for a new user. The regular bezier mode can make curves too, but not necessarily the special kind of mathematical curve which spiro spline mode creates.
It's not because of using spiro spline mode that you can select the whole path. From what I can tell, it's just a coincidence. It's likely when you were drawing the path (in regular bezier mode), and you accidentally ended the path before you were finished. And when you started to continue the path, you didn't continue it properly. So you ended up with separate shorter segments instead of a longer whole one.
I don't remember specifically whether that tutorial covers continuning a path, but it probably does. If you find it doesn't, just let me know and I'll explain. And after you go through the tutorial, if you have more question, please feel free to ask.