Regarding davening to the Lubavicher rebbe, I believe there are some who do.
And I remember an article that appeared in Beis Moshiach many years ago which said that since the rebbe can decree and Hashem will fulfill his diecree, and since if Hashem decrees the rebbe can annul that decree, therefore (and to the best of my knowledge I’m quoting the article word for word, because I found it both amazing and disgusting at the time) “Who Elokeinu? Who Avinu? Who Malkeinu? The rebbe melech hamashiach, that’s who!”
And to add a little snippet, I know someone who says (to be honest i haven’t seen him for some time so maybe he doesn’t anymore) “Baruch the Rebbe” instead of “Baruch Hashem”, and “Thank the Rebbe” instead of “Thank G-d”.
So maybe nearly all Lubavichers don’t equate their rebbe with Hashem, but there are certainly those who do.