Here is a sample campaign from my group: https://shadows-over-new-york.obsidianportal.com/ (I wasn't in Season 2, but I think life got in the way to keep it short).
As far as I know there is nothing that comes close to what you're looking for.
I read the OP's requirements and criteria, and I think of the standard IT response:
Better, faster, Cheaper. pick 2.
You can't expect much if you want it absolutely free with no ads. Programming takes time which is money. Making it look good is more time. Making it easy to use takes more time. making it user customisable is even more time. Making it well designed internally so it can be expanded upon takes time.
You get what you pay for.
That would be OneNote 2003, check Amazon but do look at The Keep as it can run on XP and off a USB stick.
Actually, if you have a Microsoft OneDrive or Hotmail account, you get access to OneNote online for free as part of your account. It's included in the apps area.
I'd like to say I can't believe nobody has produced something that can meet those four simple requirements, but unfortunately I can believe it--I just hope it isn't true.
Must Haves
1) Themes/Skins, or the ability to mimic them with uploads or settings
2) Quick and easy data entry and editing
Deal-Breakers
A) Subscription-based without a one-time purchase option
B) Overly limited functionalitye.
That's the thing, your four simple requirements aren't simple at all. You're not talking about notepad here, these are fairly complex pieces of software.
What are the main issues with Realm Works? What sort of customization is present, and is there any sort of expected customization that just isn't there? What reasons (other than pricing) are there to avoid Realm Works?

(Dungeons & Dragons)
Rulebook featuring "high magic" options, including a host of new spells.