chambers ... entries - literally, “a chamber and its door.”
by the posts - that is, at or close by the posts or columns.
where they washed the burnt offering - This does not apply to all the gates but only to the north gate. For Lev 1:11 directs the sacrifices to be killed north of the altar; and Eze 8:5 calls the north gate, “the gate of the altar.” And Eze 40:40 particularly mentions the north gate.