My plan is to open an offshore company in the Seychelles, Belize or Panama because it is just too complicated and expensive to do it where I live. Will Apple accept this kind of scheme?
You can always apply for an organization Apple Developer License as long as you have a legally incorporated company, and the territory of incorporation is one among the countries where Apple Developer Program is available for purchase.
It may be good for you to know that Apple queries the D-U-N-S number database to verify the identity of your company. So it may be a good step to check if your company can get a D-U-N-S number assigned (you can learn more about D-U-N-S by searching the Web).
It goes without saying that you should be legally able to incorporate and run the business of your company from the said territory, and from the business point of view, all Apple would see is the territory where the company is incorporate and operated from.
So, while I am not a lawyer, but if things can be taken care of within regulations, and Apple does business in the territory, you'd be fine.
Better can I have a company account without being a company?
This is neither possible nor an advisable thing to think towards. Apple has a strict verification process in place, and using any loopholes may lead to Apple revoking the developer program membership.
The app is for free and I probably will not make any money with it anyway.
Apparently it's the kind of app which requires a company to be incorporated and can't be "sold" on the App Store by an individual. You need to pay the program membership fee even if you "sell" the app for free. The fee is charged towards the cost incurred by Apple for maintaining the entire App Store infrastructure.