Through the wall hurts you...any horizontal run and then 90s cut down the effective height of the chimney...rule of thumb is each 90 is like taking 3' off the height. Supporting 10' should be no prob, just have to use the kit (or make one) that they make for this. The other thing is since the roof is so "thin" maybe you could build a box, or chase, for it to run in...that would leave less sticking out...some people think it looks better that way too. My FIL did this at the house he just built...he didn't consult me on chimney placement, just built the chase in the corner of the room...really made things difficult...it took some creativity to make it work, and even then it was just barely as far as CTCs was concerned...and they don't have a straight up pipe now either...and it cost more due to having to buy the more expensive double wall stovepipe
I'm curious how cold the weather gets where you are? Colder weather makes chimney height matter less than you would think (in my experience) I run less than 15' total stove to cap and manage fine. The biggest thing I've found with a short stack (in my climate) at worst is sluggish starts. Once the flue warms up it really doesn't know it's short.
October in the mid 40’s, November and December tail into 30’s with some days of 20’s January,February and March are 20’s and lots of times runs of teens and days below zero. Normally a breeze too especially at my house for some reason. The wind seems to help with draft though most days I think it’s sucked a split or two up the chimney
Hard to say if you could get by with a shorter stack with those temps. My stove can run anywhere from 50 F outside and lower, but doesn't fully come alive until around 14 F. When I say fully alive, I mean that's about the point where I can't tell it's a short stack.
That is not really a problem. You just cut through the soffit. Depending on the amount, I have also seen photos of where they cut into and boxed out. If you do an image search for Class A chimney you will find lots of photos. I spent a lot of time searching images when I was trying to learn what I needed to do to install my chimney.
Any 90s you introduce, including the tee through the wall install will reduce draft so you might need to compensate for it by adding a section of chimney.
Check the manual for that stove, as the measurement for the flue system may be from the floor/hearth where the stove is sitting. If so, you just gained over 2' (not sure how tall the stove is). Oops, it almost 32" tall. That's how it is with the 30NC.