Mostly. It is possible to distribute applications to jailbroken phones without Apple's help, but that's a minority of phones. When a new version of iOS comes out, a new method of jailbreaking usually needs to be found.

Stock phones can only install apps from the app store, or apps signed for that specific device by a developer. Developer signing is also controlled by Apple, though.

Absolutely. The only other way is through the Cydia app store which requires a jailbroken device, or with a nifty web app.