when the internal ssd is taken out I can boot, which makes the ssd most likely suspect.
Most likely the SSD is the issue. There is always a slim possibility the Logic Board's SATA port/controller has an issue. Your WiFi issue may indicate other issues though. Figure out the WiFi first.
wanted to try and boot from external drive, have actually done this with a backup drive from my 2012 MacBook Pro running high Sierra. Boots fine but there is no Wi-fi.
connected a correctly formatted external drive, booted to recovery.
spinning globe and asking to select network, click the drop down and select my network, enter password, starts to connect.
when ready to install OS asks me to connect to network but no networks showing?
It appears you may have a WiFi issue or possibly a loose antenna cable on the WiFi card since it happens booted to two different OS. Can you option click on the WiFi icon in the menu bar. The Signal should typically be somewhere in the -40 to -55 db range. The Noise is usually around -85 to -90db.
The last photo looks like you are booting into either Lion or Mountain Lion. I see the lion icon in your screenshot. Is your external drive just a freshly erased drive with nothing on it? Did you ever install OSX 10.12.4+ on this laptop? If so, try booting into Internet Recovery Mode using Command + Option + R which should in theory boot you into a Mojave installer. FYI, we recently encountered a 2013 MBAir which for some unknown reason would only boot into Yosemite IIRC regardless of the keys used for Internet Recovery Mode.
Maybe you should get a Thunderbolt to Ethernet adapter to connect the MBAir directly to your router/modem for your test. If the WiFi issue is not a loose antenna cable, then you may have other issues with this laptop.
Run the Apple Diagnostic. Note that a passing diagnostic does not mean there isn't a problem. It just didn't detect any issues at the time.