I have a small scripting project that consists of five different source files in one directory called \"Droid XX-XX-XX\". Each time I created a new backup copy of the source
Now that I know a lot more about Git, I can answer my own questions.
It would be better to do a global search-replace using regex to standardize the whitespace between all the files across the different versions of the project, so that when they are sequentially committed, the whitespaces changes won't need commits. That being said, Atlassian SourceTree's diff tool allows you to hide whitespace changes, so at least you won't see those.
The key to deal with filename changes is to make a commit where only the file's name changes (don't stage any other changes). Then make a commit where its contents change. That way, normal diff tools that don't do a ton of heuristics and deep digging can make sense out of what has happened. The problem is that if too much changes about a file, like the name AND a lot of the contents, then most diff tools will treat it as a summary deletion and new file. (as mentioned in the correct answer)
This is a tougher one, there's no really good way around it. If you split up a file into two, or merge two, it will just be ugly in the diff. Try not to make lots of changes at the same time as doing the split, so that the split will be one thing, and subsequent changes will be another.