No, Apple just forces all development for their device to be with their dev kit only, and tosses out any app created with a different dev kit such as Adobe even if it produces the same code.
Not illegal, as they are enforcing the terms of their store that the developer agreed to.
Apple allows competing apps on their phones but cripples them in comparison to their own favored apps.
Citation needed. There are plenty of apps that do better than Apple's versions also on the store.
Apple forces all app purchases to go through their app store and there is no other method of installing apps on their devices.
False. See: any MDM provider and enterprise app distribution. And no, you don't have to use an OS X Server to do it. See: AirWatch, MobileIron, etc.
Apple actually is a convicted monopolist on rigging book deals to screw Amazon.
Which is in no way relevant to anything even close to what this is about.
And you still haven't read about what the EU is actually doing here - the current antitrust complaint is about SEARCH and not Android. They are starting a separate antitrust investigation into Android regarding force-bundling of Google services with Google Play, but no formal complaints have come out of it yet.