The image of Laura's doppelganger (in ep.29) and the image of the woman,who looks like Laura(in Cooper's dream) are one and the same,yeah.
And about the backward talking,I don't think it shows someone is a Doppelganger.Everyone in the lodge speaks backwards(except Cooper).I think that this girl in Cooper's dream(with the vision of Laura) is a projection of the lodge,just as Windom Earle,Annie and Caroline,we see in ep.29.they speak backwards,too,but this doesn't mean they are Doppelgangers.
Beware of BOB
When I call out no one can hear me,when I whisper he thinks the message is for him only..my little voice inside my throat,I always think there must be something that I've done or something I can do...But no one no one comes to help,he says,a little girl like you...
...I think the Doppelgangers we see in the lodge are the following : Laura's doppelganger,Leland's,LMFAP's and at the end-Cooper's,although we see Caroline's white eyes,I don't think it was her Doppelganger....just a lodge presentation,in order to confuse Cooper and to make him weak...
