Delica Canada | Mitsubishi Van Club

Hey, I'm a brand new delica owner so this might be a newbie question. Looking at where my EGR is supposed to be I see a plate bolted onto what I assume is the input side(?). The output side of the EGR is not blocked by anything and I'm wondering if this could cause any issues?(PLEASE SEE ATTACHED PHOTOS) On-top of this there is a hose on the back wall that is not attached to anything, covered in carbon and has a hole blown through the side of it. It's connected to the top of the engine block and from what I've seen in other pictures it looks like the end should connect near the air filter housing(bolt stuck in place in second photo). I'm guessing that this is part of the EGR assembly but I'm not sure and I'm also wondering if this detached could cause any issues for my engine?

Overall my Delica feels very happy, starts up great in as cold as -5c, and drives great. The only issue I have noticed is that after a cold start the engine will run fine but after 5 minutes or so she will idle rough and cough out smoke. This only happens before the engine warms up and the van idles very stably once my coolent temp gauge reads warm. Yesterday I checked my glow plugs, they're all in good shape and looked over my injectors and could not see any carbon build up around any of them. I'm wondering if this is something to be concerned of or if it's normal for a diesel Delica in a colder climate?

I'm already in love with my Deli and any help would be much appreciated!