An unusual question: is it possible to somehow take a photo from a locked phone, just as it's possible in iOS? (you can take a phone even if the phone's locked but you still can't browse the gallery)

Do you mean locked as in swipe-the-ball, or locked as in put-in-the-password?

Swipe-the-ball: just open camera-cover, and you will have auto-unlocked device with auto-started camera. No hassle.

Put-in-password: that's osso-systemui-devlock, if I remember correctly. It's closed source, and, unlike osso-systemui-tklock, not reverse-engineered yet. If you, or somebody else, reverse-engineers it, there could be additional features added to it.

osso-systemui-devlock-dev is already open-source, in CSSU.

Best wishes.