Brand limit and detaching question

If I have a brand limit of 3 and asuming all 3 of those are Attached to a target so that when I cast a new brand (going over my limit) does the Brand that gets removed count as being detached?

Additional question, the mastery "Brands Attach to a new Enemy each time they Activate, no more than once every 0.3seconds" is the last part a global cooldown for all active brands, or does each brand individually have this 0.3 second cooldown?