Is it possible to update free apps from another account? By what I've already read, I know that if you have purchased an app in the Mac App Store with the account X, then you can update it only by logging into X. Now the question that arises is: What if the downloaded app is free, does the same rule apply or not?
Yes, the same principle applies. For Apple, it is a purchased product, though in one case the price was $0.
So it's not transferable from account to account. As a developer, I know one normal case that is: the app is free for one day. Then the app turns paid. If a user could transfer to another account, then it would be a problem for the dev since it may be transferred to anyone.