I don't know the version of adb included in the link I posted. But, since the link is for Google and was updated in June 2017, I believe it will be the latest adb.
I am not sure about the error you are getting when you launch adb. Are you trying to launch it from the filer explorer? It's a command-line utility, so you have to open a terminal window, navigate to the folder where you extracted the tools, and run adb from there.
You use fastboot to install a custom recover (TWRP is a custom recovery). Once TWRP is installed, you boot your device into TWRP and use adb to either push a custom ROM or sideload a custom ROM on your device. You can also either push or sideload other items, such as GAPPS, if you want Google Play Store and other Google apps on your device.
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