You are dealing with soft sludge, not tree roots. A snake will poke a hole through the sludge, but it won't clear the walls. The water will drain for a week, then clog again.
I know, I know. It smells like a meadow. But liquid softener is basically wax. It coats your clothes, your machine, and your pipes. Use white vinegar in the rinse cycle instead. It softens fabric and dissolves alkaline sludge.
No, not literally. But you have to remove the washing machine standpipe trap. Usually, there is a cleanout plug just above the trap. Remove that plug (have a bucket ready). Go in with the auger downstream toward the main line, not upstream toward the washer.
Your washing machine is incredibly strong. It pumps water out with force. If the water isn't leaving, it usually isn't because the pump quit; it’s because the water has nowhere to go.