You are pretty fucked up.
Regarding rotator cuff, i had a partial tear on the right side. Even before the tear i had to inject a painkiller everytime it was chest or shoulder day.
Besides therapy, the only thing that allows me today to still work out is to do everything underhand grip; bench press, lats exercises also. Dumbell press with the palms facing each other, also on shoulder press movements. Never do front bar squats.
Plenty of videos on the net about the subject, basically training like this removes stress from the rotator cuff.
About the lower back, check a doctor ASAP, if it's a herniated disk it's wise to "repair" it as soon as possible.