Point One: This will have nothing to do with EU regulators because Apple does not have a dominant position in the market.
Point Two: Even if Apple did have a dominant position in the market, it still would not fall under the jurisdiction of the EU regulators because Apple makes the hardware and the software; it does not build software for OEM phones. Therefore, the market is not the iPhone; the iPhone is in the same market as Android, WinPhone etc...
What then was wrong with Microsoft bundling WMP with Windows? After all the market wasn't Windows - you could just have installed Linux. Or uninstalled WMP. Similarly for IE. What about Google's alleged manipulation of search results - you could just have used Bing? Surely actively preventing a competitors software functioning on an important and major platform is far, far worse than using a major platform of your own to promote your own products? (Of course I'm no anti trust lawyer... but if this isn't the law it should be.)
(If one were cynical one might think that Apple is trying to push custom towards iCloud...)
All MS has to do is what everyone else does: run the signup outside the Apple store.
No You're not allowed to link to outside webpages when money is potentially involved. You can buy SkyDrive subscriptions from the SkyDrive website therefore the app cannot link to the SkyDrive website. And I really doubt MS can be bothered to bring the live ID sign up process into an iOS app.
Even if this were possible, I'm not sure it would be wise. Hiking the price by 30% would probably raise their price above competitors such as Dropbox, in which case I'd just go for Dropbox.
As an interesting side note Dropbox have faced similar problems (and resolved the problem by removing the ability to sign up for an account from iOS app login page). Doesn't lead to a nice UX for first time users.
The apps mentioned in the articles used a non-native login and/or a sign up link that took the user outside the app. They were not rejected because they use Skydrive; they were rejected because they broke the app store rules. If they'd connected to their own in-house service they would have been rejected anyway.
There is, afaik, no other way to use SkyDrive. There was nothing inherent about what they did that broke the app store rules beyond, if you clicked through enough links from the sign in page, you could eventually arrive at a page at which you could make payments. And this does affect other services (dropbox, for instance). (Of course the fact that Apple offers their own competing service clearly can have NOTHING to do with this decision...)