What can be the reason for "internet may not be available" though the IP address was got
Strangely, this advice from 2016-09-14 concerning the WiFi router configuration helped:


  Inside the router configuration (e.g., accessing the IP 192.168.1.1), change the "Group key update" value from 0 to 30 seconds, under the "Wireless > Security" configuration, right below the WPA-PSK/WPA2-PSK item.
  
  Router: TP-LINK TL-WR740N / TL-WR740ND.


(My router model is different.)

I'm a bit worried that 30 sec as the group rekeying interval is the minimal possible, whereas the recommended value is 3600 sec (1 hour), as I've read on the web.

But for now, I haven't yet tried to experiment with since it began working. Also, I have left the static manual IP configuration instead of DHCP on the Android device (matching the reserved IP address for this MAC address manually in the router settings), although this alone didn't make it work. (But I'm not changing this, unfortunately for the experiment, because I don't want to break the current working state.)