Creating and managing a Facebook app from a Business Account
Can I create or manage a Facebook app via a 'business' account?
When I try to access https://developers.facebook.com/apps when logged in as a business account it redirects me back to my homepage and won't let me create an app.
Context: A business / advertising account (sometimes called a 'gray account') is a special, now-deprecated type of account Facebook provided to advertisers to manage their Ads and Pages before Business Manager launched - the primary reason people want to use a business account with an App is to link the existing App to the Ad account so Ads can be driven to the application.
Is there any way to manage or create a Facebook app using a business / gray account?
'Business' or advertising accounts can't manage apps - if at some point in the past you were able to create an app using a business account this was a bug or loophole and shouldn't have been possible - only real verified user accounts should be able to create and manage apps.
It's also possible to have a Business account which owns apps if you created a fake user account, created apps, and later converted your user account into a business account or had Facebook do it for you.
If you need to share ownership of the app between multiple people
You can do this by making all of the admins/developers working on the app developers or admins directly via the API or the 'Roles' tab of the App settings: 
If you need to run ads for the app using a business account
You can specify which business accounts will manage the ads for an app in the app settings on the Advanced tab - add the email address used to manage the ads.
This is the only supported connection between apps and business accounts.
Screenshot below:
Strictly speaking I'm not answering the specific question you have at the end about gray accounts, but answering the bigger overall question about business accounts in the new world.
Since the original question was asked, Facebook has introduced the Facebook Business Manager which enables businesses to have a single place to manage pages, ad accounts and apps .
https://developers.facebook.com/docs/apps/business-manager
You login to the business manager via your facebook login, but it can have a business email and name etc. associated with it. The administrators can add other people and modify their permissions, and it keeps peoples business identity and personal identity separate.
Significantly, if you have more than one app and they are associated with your business via business manager, you will get the same User ID for a given user whichever app they are using. If you don't do this, you won't, because the User Id is normally scoped to each app.
So this new world gives the benefits that a) apps can be managed via a business identity b) apps which belong to the same business can report the same User Id, which makes it easier to track and co-ordinate activity by users across several of your apps.
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