aircraft should be at the same circuit height on the downwind leg. Also, they should be in level flight, not one descending over another, in each other's blind spots, as required by an overhead join.
Yes, the circuit height (or altitude) should be respected when entering (the beginning of) downwind. That's why I was taught to cut power after making the overhead call, to ensure a quick descent. After some marked experiences, mainly with helo's on training, I learned not to go direct from overhead (the signal square) to (beginning of) downwind, but rather to descend along the circuit, i.e. upwind and crosswind legs, and zigzag slightly so as to keep an eye on departing traffic below.
But again: this is beginner's talk.