For the questions, you asked here are my comments :)
1/ Any ideas what could be wrong ?
-> There would be nothing wrong with the config maybe you just misconfigured something so the best thing to do is to re-setup everything you can restore the router settings to factory defaults in System > Administration > General Lowest part you will see Restore to Factory Defaults.
2/ When selecting WiFi(WAN) to ”Main WAN” and then ”Save”, the "Scan" button appears. When scanning, some public WiFi:s don't appear ? But they appear in my Apple devices. Why ?
-> RUT240 is working in 2.4Ghz with the IEEE standards 802.11 b/g/n. So my guess would be the device is running on 5Ghz WiFi which is why it is not showing in RUT240.
3/ After you selected a public WiFi and the connection works you maybe want to change the WAN port to a LAN one. Doing this RUT discards the newly scanned connection and you have to scan again. Bug ?
-> The proper way to set up this is First you need to select the Main WAN to be on the WiFi network or Mobile you must untick the Wired WAN to prevent issues. Next is to navigate to Network > LAN > Advance Settings then Use WAN port as LAN. Now return to Network > WAN then Scan for the WiFi network (Note: You will only see 2.4Ghz WiFi SSID.) Then Join the network and Save Config.
Let me know the results