With regard to bleeding, I overhauled my rear caliper recently and when reassembled, had great difficulty getting any firm pressure on the brake pedal, even though there was plenty of fluid coming out each time I bled it. Tried this for ages and in the end I unbolted the caliper with the brake hose still connected, turned it around slightly, and bled it again whilst holding upwards in hand.
Several bubbles of trapped air came out and the pressure at the pedal was fine.
Just mentioning as may be useful to someone if they are having the same issue.