For rear of stove connection. You must be able to access this part for sweeping; if your stove is in a recess you must have large left and right air gaps to facilitate access and sweeping.
As with all vitreous pipe the bottom end narrows to a lesser diameter to enable insertion into other pieces of pipe (male is always on top). Key reason is that any condensation that trickles down inside pipe cannot escape. Straight lengths can be cut using a grinder and 115mm cutting disc (available from this online store).
I assume that the door referred to on your "5" Tee with door" is on the bottom of the tee. Am I correct?
Yes the door is on the bottom :-)