Regarding the culture bit: I feel that Erin Meyer's "The Culture Map" [1] should be high on any reading list around how to work in a remote environment, especially as a manager. Of course, every individual is different and not everything needs to be taken at face value, but it provides a nice framework to think about how/why other teammates may approach situations in a specific way.
[1] https://www.goodreads.com/book/show/22085568-the-culture-map