Does ritual impurity transfer from the hand to personal items (comb, oud oil, Vaseline, olive oil)? And is it permissible to use them afterwards? And does ritual impurity transfer from the foot to the bathroom floor and slippers merely by contact, or not?

There is a difference between the presence of a physical impurity ('ayn an-najasa) and the presence of its legal حكم (hukm an-najasa). If the physical impurity is removed by a liquid, but its legal ruling of impurity remains, then this ruling of impurity does not transfer, as stated by the Malikis and others. Some scholars, such as Imam Abu Hanifa, and in one narration from Ahmad which was chosen by Ibn Taymiyyah, held that if the impurity is removed by anything whatsoever, its ruling also ceases. Therefore, if the physical impurity is removed from the hand, and then something like a comb or oil touches it, the impurity does not transfer. As for the assumption that the ground and sandals have become impure, this is incorrect, because the fundamental principle regarding things is purity, and they do not become impure by doubt. It is advisable not to be overly meticulous in such matters, as they are among the Devil's entry points and lead to obsessive whispering (waswasah).