The account is free, yes.
With the help of C’, a Microsoft Global Escalation Services representative – we were able to recover the account.
Microsoft requested details not only about the mentioned Microsoft account but about the Bizspark program associated with it, and after we supplied the full details, they have removed the account suspension.
We haven’t managed to understand why the account was suspended in the first place, nor did we managed to get MS to take a look at their ticketing system (which still shows tickets of other MS users). Investing a month in trying to get answers is more than enough. Let’s hope our tickets are not available to other MS users… let’s hope yours isn’t, as well.