On Windows I suggest Tera Term instead of PuTTY. It is very simple to use. Open Tera Term, on the first screen enter 192.168.1.1 as the Host, leave the rest as defaults and click OK. On the second screen enter user name is root and type your password in the passphrase box. Click OK and you should be connected.
Backup OpenWrt configuration
You can backup your OpenWrt configuration through the web interface via System > Backup / Flash Firmware > Generate Archive .
Don't know how (what kind of file) you can download it to your Pc and analyze it
It is a tar file which you could open with 7zip or natively in Linux.
But being able to ssh is extremely useful.
I also had a Dir 600 B1 and it had the same problem, when I configured it as the main router my modem in bridge and the router in PPPoE protocol; the LAN connection without problem but the WiFi did not give Internet access to my devices until I completely rebooted but after a while the same thing happened, the solution I found was to build a custom build and remove the packages and library not necessary to give it a little bit of CPU relief and that was the solution.
I currently use it with DD-WRT which is the firmware that is most stable for the Dir-600