>Do people actually write eBay?

Yes?

In my experience, publications and the like do tend to respect the capitalization and other choices of a company/project/etc. with perhaps some exceptions like the ! in Yahoo! and perhaps all caps as in NVIDIA. In the case of Wikipedia, I'd go so far as to say that they're simply wrong if they're ignoring the actual way a company name is officially styled.

Mind you, I'm not necessarily a big fan of case-sensitive everything but here we are.

You'll see me even write e-mail!

Names should be written as they were created, grammar regarding them only comes into question in case of suffixes or the like.

I can mostly agree with people's names, especially stuff like cultural variations or things that are basically name prepositions like de/Mac/o etc. That said if you decided to change your name to "JOHN SMITH" don't be surprised if that decision was less respected and you were referred to as "John Smith" following capitalisation norms.

Companies don't get even that assumption for me, sure I'll use "iPhone" because they've won that one and it's the cultural expectation, but the only time I'm using "FREE NOW" is to criticise that decision

Maybe. Probably. But in practice no one really cares other than editors and pedants. I'd probably only bother if I was showcasing something to people from that particular entity.