Can you confirm if this issue still occurs with the most recent release? If so, are you able to test the world folders on a different device?
I can confirm that hitting chat/menu buttons while breaking blocks continues the action, however I am unable to replicate the movement part. Is the movement still an issue in 0.9.4/0.9.5?
Does this issue still occur in 0.9.4/0.9.5?
If so, are you able to remove your world save files through File Manager?