Q1 Windows airport utility is well out of date albeit still works OK mostly.
Is your Airport the tall tower model.. that is Gen6 AC model.
If it is flat pizza box looking one it will have a number on the base, A1xxx either on paper label or moulded into the rubber.
(There is a model number on the Gen6 base as well but very hard to read)
Also in the old version airport utility.. I am using the Mac version but same thing.. if it is the Gen6 Extreme you will get this error. A newer version of the Airport Utility is required.

Q3
You need a wireless analyser of some sort. Lots of them available. Just look for a free one.
Mac OS has it built in but I also run netspot which is available for PC.

I have a couple of routers.. but you can see the Airport (Time Capsule in my case).. 2.4ghz is very good this morning for some reason. tc5e and you can see further down the list tc5e5ghz.
It is important to track the signal strength and channel. Mine is using channel 36 and is giving me a signal of -50dBm at the computer.
You can also see the signal at the router by going to Advanced, Logs and Statistics, Wireless Clients.

Q4
Hold in reset before power on.. keep holding in reset for 10sec after applying power.. the unit will start flashing amber rapidly which means you did it right.
Redo the configuration. Make sure you use short names, no spaces and pure alphanumerics.. NOT APPLE RECOMMENDED NAMES. Passwords same rules but 8-20 characters. Do change the wireless name even if you previously had it conforming to rules above.
You can set wireless channel. I often do this for 2.4ghz but 5ghz is a bit different. There are a bunch of channels called DFS you cannot access manually. It might be worthwhile though to fix the channel as well, e.g. 149.

Go Done and then update to apply the settings.
IMHO one of the problems can be the Airport swapping to a DFS channel that a client cannot use or has problems.
You can also do this using the airport utility in iPad or iPhone. IMHO the layout is incredibly messy but it will work better than PC version.
If you continue to have issues get a new router... today.