I'll throw something at # .5
I can't speak directly for the 1019 but don't assume that your receiver won't drive 4 ohm speakers just because they are not rated for it. It is rare that you will find a receiver company actually state that it is 4 ohm compatible even when most are as long as you are not pushing ridiculous volumes. They are just being overly cautious in many cases, although there are some models that have displayed problems. Your room is not very big so you won't need to push things at all to go as loud or louder than you need.
Someone else may be able to help out specifically for your model. Somewhere buried by the search feature, is a list from Axiom of recommended brands. I forget where Pioneer sat but a call to Axiom would clear it up for sure.
#1
You have a pretty good sub and again your room is not huge so I suspect that you would be Extremely happy with M22s for mains and be able to keep your screen width intact. I have not heard M22s but people here repeatedly compare M22s and a good sub as being very similar to M80s.
#2
I don't believe in putting even even low voltage wires under carpet but many do. I'd prefer to hide it behind baseboards
and such as they are easy to remove and replace, if you are very careful. If you really need to go sub carpet, try to keep near the edges of the room and other places that are less likely to be walked on. Even if there is minimal (but possible) fire hazard, a short could be hard on your equipment. I'm unsure what going with a flat wire brings to the table for durability but it might be worth looking into.
#3
I'd say start with none and try it for a while. If you feel your bass is lacking or it's weak in certain areas of the room but boomy in others, than you can try some bass traps. There are lots of good articles and posts on purchasing or DIY solutions. From there, you can tweak forever or just sit and be happy, depending on your personality.
#4 Neon nailed it.
Now that your already obviously hooked......
Here is a good article on impedance that is good to know when choosing a receiver/speaker combination.
Speaker Impedance 
