1. I read Matrix Search like "Google on crack" or really sophisticated database search algorithms. I would say if you don't have their commcode, Matrix Search might get it, or get you to something that might know it (some public social media site, or a site with private data that you have a worm in or something, or they put a review on Yelp with their real name, etc).
But finding something in meatspace is covered by using Trace Icon on a marked target. Once you have a Mark on it, you us Trace Icon and you know where it is in the meat world.
2. Just their name? Hm, it depends. If they're not running silent you might be able to find that with Matrix Perception, possibly extended. If they're running silent, then you start there. Once you locate their commlink in the Matrix, you locate them in the meat with Hack to Mark it then Trace Icon
3. Again, I don't view Matrix Search as doing that. Matrix Search to me is Google search on crack. What you're describing, looking for smart links, is more Matrix Perception to me. If they're that far away, you take Noise penalties or can't see them if they're running silent (IIRC). The whole deal with the 5e Matrix is needing the decker on-site, and I'm all for it.
4. Unless it's running silent, yes, but then it should be easy to find. Or you just plug a cord into its data port since it's right there and don't even deal with the Wireless Matrix. I believe your 2nd and 3rd entries are correct.
5. Hm, I'm not sure. My suggestion would be using direct cable for that, but you could look for data and cross-reference the location of this door on a schematic or circuit plot of the floor and open the corresponding door.