Fed, yes pics of pre-foam, especially at very top of underside of roof, where the shallow pitch roof rafters of addition are attached to opposite side original rafters. If they do.
1st pic, this series, does look like wall supports ceiling joists, if that is all it supports, it is not big problem as far as door opening itself.
2nd pic they kinda look like they slope, is addition ceiling flat or does it slope? I and ,I think, mae-ling have suspicion the ceiling joists, or "beams", are also roof rafters. ( shudder)
1st pic; that "triple cap" is sure constructed strange. Looks like a series of headers on jack studs with no real top plate. The king, if thats what it is just goes up to...rafter? Is it under a rafter?
Does that 2x4 sticking up continue on down to floor? Or does it end just behind that old rafter? It looks like it could have been extendended to hold ceiling joist. And you say joists are just sitting on wall unattached?
Pics 2 and 3 are opposite ends of the collar ties? ( The horizontal 2x's between steep old rafters?) I may be getting idea why the rafters were cut off and fastened to wall, somebody was worried about rafter spread in remaining old wall. That could also explain studs running up to new rafters. Though that could have been done by extending collars out to top of wall. Or just wanted to keep balanced looking sloped ceiling. possibility of old cut off rafters not
being load bearing increased.
Fed once you get all the down stairs load bearing and other structural things
checked out, you probablly can " extend the beams out" and get wider ceiling, more head room, and avoid the head level, head banging tunnel effect at new opening. If rafters have to stay, you may be able to devise way to cut them at wall height level, replace those collars with stronger beams running under rafters, on top of strengthened wall, over addition ceiling tie into to far ends of shed roof rafters or opposite wall.
Do not get frustrated that every answer seems to open up more problems. This is way simplest, most inexpensive, remodel jobs usually go. Take solace in fact that you have given us interesting puzzle to ponder.
Some one strips wall paper to slap on paint, termites chewed dry wall paper, remove drywall, they chewed stud, remove stud, they chewed plate and sill, blown in insulation has settled to lower 2 feet of wall. Might as well replace it while drywall off, in fact do whole wall, strip drywall, this wiring don't look good. There is no stopping place.
Speaking of puzzle, well some one was, sometimes it seems easiest way is take house apart, start all over. Every time we leave our house, mrsnot hopes tornado comes along, makes one quick dip and tears it down while we're gone. You could forget about opening, add exterior staircase to get into that room.