Did she do the test outside with her back to the sun and the tube held waist high? I doubt she did and that is how to do the test so yours is more accurate. There is a YouTube video on how to do the test if you are having doubts.
The request for a picture was to help me see if it was above or below the waterline as that effects the repair. Above the waterline you could use almost anything, below your choices are limited.
Most vacuum installations recommend turning off the main drain or turning it almost off to avoid it getting stuck. I turned mine almost all the way off and my doesn't get stuck. I figure the vac is already sucking from the bottom of the pool so in essence it is acting as the main drain.
There is no way for us to tell exactly what each valve does. I can tell you the everything before the pump is suction and after the filter is a return. You will have to turn them on and off one at a time to check where the flow is coming from and going to and then label them.
You need to add some chlorine and some CYA. And what is your PH number?
Use pool math to determine how much of each. Until you get CYA in there you are going to go through liquid chlorine quit quick.