For me, it's easier to set the launchoption "-log" in Steam. This will open up a seperate window each time you launch BL2 where you get the same output as in the console in the game. Makes it a lot easier for me to copy results without navigating to the log-file.
Example here:
Yes, they don't. You can just have a file "patch" in your "Borderlands 2\Binaries"-folder and you can execute it by typing "exec patch" into the console.