Apple - Symbols appear instead of letters/numbers when typing on Mac
Your qwertyuiop result indicates that your machine thinks that both option and shift are being held down while you type. The symbols are not random but exactly what is supposed to happen when those keys are depressed. Normally this would indicate a damaged keyboard, especially if you try another one and it works ok.
I just ran into this issue myself. Was able to get out of it by hitting [option] [caps lock].