Okay, the first flight is easy, as * Gold you will have lounge access in Manchester since it is after all an SK-flight (even if codeshared as BT). When you get to Copenhagen you may of course try your luck but I would guess the answer will be no (though I think I read somewhere that * Golds have been accepted when flying BT). In Riga, I am afraid the answer will be no.
All this is of course very stupid, considering what goodwill it would generate for BT to offer lounge access to * Golds, wonder if it really is their intention or if it is the other carriers imposing these rules on non-star airlines?