Neither the second nor the third ability of Hero of Bretagard refers to a specific kind of counter. Any counter that's on it will do.

Hero of Bretagard has recieved an update to its Oracle text. Specifically, its triggered ability doesn't care which player is exiling the cards and permanents. Cards put into exile from your hand for any reason, such as the foretell ability, cause the ability to trigger, and permanents exiled from the battlefield cause it to trigger if you controlled the spell or ability that exiled them.

Hero of Bretagard's triggered ability will trigger when a spell or ability you control exiles any permanent, including token permanents and permanents you don't control.

With ten or more counters on it, Hero of Bretagard will have flying and indestructible, and it will be an Angel and a God (and a Human and a Warrior, but those aren't as exciting).