Does anyone know which room this is and perhaps more about Rasputin's visit there.
It might be the nursery. In Douglas Smith's Rasputin
there is a photograph of Rasputin in a room which has a similar wallpaper. Unfortunately the photograph is too small and the quality is not very good, so it is not possible to say that it is the same.
The photograph has this caption:
"Rasputin in the palace nursery surrounded by Alexandra and the children, from approximately 1909. Alexei's nanny, Maria Vishnyakova, sits smiling, lower right; to her right, a glum Tatyana and a happier Maria, her bare feet peeking out from under her white dress. Olga stands on a piece of furniture behind Rasputin."
From the same book:
"From Rasputin's own letters to the children we know that he did visit them in the nursery and that they engaged in play and even some roughhousing. He wrote in February 1909: "My dear golden kiddies, I live with you. My sweet little Alexeiushka and kiddies, I live with you and often recall the nursery where we lay about. I live with you. I will come to you soon." He would write them brief notes on the importance of faith and love and the need to trust God's mysterious ways: "What matters is not the power, but belief and love [...] The paths of God are inescrutable; it seems things are bad but then they turn to be holy" He wrote to them often of the beauty of nature, as in this letter to Maria: "My dear pearl M! Tell me how you talked to the sea and to nature. I miss your simple soul. Will see you soon. Kissing you from the bottom of my heart."
He would try to comfort the children, and Nicholas, when their mother was ill...."
Douglas Smith, Rasputin