It sounds like reflux to me, along with some self settling issues.
I dont know much about reflex, none of my girls have suffered it. Is there a nurse, doc you could talk to further about this?
In relation to the sleep, my 18 week old has 2 x 45 min naps a day - if im lucky- and will sleep from 7-7 am with 2 feeds during the night (usually 1am and 5am). Somedays she goes ALL day with no sleep, just catnaps here and there usually in the car when im running around picking up DD#1 from kindy. It sounds like the midnight to 3/4am sleep is due to pure exhaustion...poor little thing...(and poor you !!) . I have noticed if i dont wrap her, she takes longer to go to sleep.
I think bubs wanting to suck constantly is a pretty normal thing. I wish my DD would take a dummy. SHe wont, but sucks her bottom lip.....she too always wants to suck...
I think maybe a lot of the sleep issues your little one has may be due to refulx...do you think??