Khvicha,
First thing, I do really admire your way of typing a post, very detailed!
Now coming to your issue, specially when using WAMP (Windows + Apache) (This combo you may never find on Production environment) when filling in admin details after installation, either screens gets blank or nothing seem to happen after you click submit button.
This usually happens when cache's get corrupted during install (again, I have only experienced this on a Windows + Apache combo), all you have to do is, go into your moodledata folder, and delete the "cache" and "localcache" folder, refresh browser and hopefully this issue will be resolved. Dont worry about deleting the folders as when you click refresh, they will automatically be re-created.