First question: which engine type are we talking about?
1. It can be installed the wrong way, yes. Apparently you experienced that.
1A. I do not think so, because air near the heater valves will not come to the t-stat area without engine running.
Did you switch the heater on so that on both sides the coolant could circulate?
2. Aux fan should come on. Check it. Could be the relay. Pull the aux fan plug and bridge it, it should then run on low and high speed depending on the bridging. I had that some weeks ago, only low speed was running. In this case the relay did not switch to high. See Bentley for checking that out.
Also go to my website and then the link to Gale, there is something about faults with aux fans.
3. You answered it already, you need something to work on and be the happiest man in the world when it works what you tried to repair. ;-)
4. This is the ultimate testing method
http://www.mwrench.com/Whitepapers/FanClutchtest.pdf