1. To get my desired outcome, will this be the best setup or is there a shortcut. (External HD connected to media player via HDMI, Media player Audio Connected to Receiver via digital Coax or Optical cable)
Yes. That sounds about right.
2. Is the 5.1 matrix sound also dependent on the movie file? Will the 1080p usual downloads capable of this? Can the receiver mimic this outcome?
You need to check whether the 1080p encode is in 5.1. In my private tracker, you know its 5.1 because it is included in the filename. Without "5.1" in the filename, it means its in 2.1.
With the well known scene releases on public trackers, they post the information on the torrent page.
3. What receivers and speakers do you recommend and around how much? I have a very limited budget and I am looking for the cheapest possible option. I'm not looking for the loudest or powerful sounds as we will be living in a condo. I just want to achieve the surround output.
Cheapest would be HTIB. However, if you would like better sound, get a pioneer/yamaha amp and wharfdale/anthony audio speakers.
Personally, I would put most of my money in speakers and go second-hand with the amp. Maybe you can go for Dali Zensors, Monitor Audio bronze or Polks.