The things you are talking about changing are pretty fundamental to org-mode; basically you are trying to change the org-mode syntax. The reason why Header 1 in your example is not being dedented, is that org-mode does not see it as a headline, because headlines by definition start with leading stars. Also, while it is technically supported to use * to identify a plain list item, this is not recommended, and can cause some unexpected behavior (see footnote 1 here).
That being said, you can have some control over the appearance of headlines. For example, you can use the org-bullets package. You can then define the bullets to use in place of * like this:
(setq org-bullets-bullet-list
'("◉" "◎" "⚫" "○" "►" "◇"))
which will define the bullets used for the first six levels of headlines. You can replace the bullets in that list with other utf-8 symbols, and you can even use " " as one of the symbols, so that your Headlines will be preceded by a single space. However, note that this only affects the way headlines are displayed; they will still be preceded by * in the actual file.
I know it is not very helpful, but my overall suggestion would be to stick with the org-mode syntax if you want to use org-mode, i.e., use a structure like this:
- List one
- List two
* Header 1
- List three
- List four
with * starting a headline, and - starting a plain list. Since org-mode files are just plain text, the magic of that mode depends heavily on those files having a set structure. In my own experience, if you try to change that structure (another example is changing timestamp formats), it will cause more headaches than it relieves, and cause a lot of the functionality that makes org-mode so great to break.
Just as a side note: I prefer a cleaner view as well, and one option I like to enable in addition to org-indent-mode is (setq org-hide-leading-stars t), which will display only a single star/bullet per headline (although the leading stars will still be present in the actual text file).
