If community manager has removed my account from a StackExchange site, such as Arcade.SE, then has it been totally removed from SE's databases, or has it merely been marked as "removed"? In other words, could police, for instance, access that data when they request?
Well, those are two really different questions...!
Yes, deletion means your account is removed from the database. That's your account on the site where you requested deletion - the entry in the Users table that once represented you and linked together all of your various actions on the site is hard deleted and cannot be queried for or restored.
If the police / someone with legal authority (court order) want to know something about an account - even one that's been deleted - they're probably going to get it. Like any self-respecting website, we have logs and backups that could be used to piece together enough information on a deleted account to essentially recreate it. Not to mention the public data dumps that we publish periodically which anyone could be squirreling away for later use. I'm neither a lawyer or a security researcher, but as a general rule: if you're doing something in public that you're afraid might come back and bite you later on, it's probably already too late to start worrying about covering your tracks.
Note that because they're hard-deleted, actually restoring an account in a form that would allow you to log back into it as though it was never gone would involve a ridiculous amount of manual work and if you ever ask for this we'll point and laugh and tell you "no". The posts you've written are still around on the site, and if we can verify you wrote them (not always possible) you can have attribution restored - but almost everything else attached to an account isn't and can't be.