Yep, you can leave your fish in qt for that long. It's really the only way to be sure whatever is in your tank is dead and no longer a threat.
Since you will be treating the qt I think it'd be ok to use your tank water, maybe a half and half split between tank water and fresh saltwater.
Whatever you put in the qt will be with the fish so I;d limit it as much as I can. And with the qt make sure no sand. The parasites can linger in there and it will be easier to clean the qt tank as well. You will have to monitor the qt though, quite frequently especially if you don't have it cycled. I woudl imagine daily water changes might be necessary to keep ammonia levels down. :-( and you also have to monitor the medication levels, too little and youre wasting your time too much and you risk your fish.
Petco was still running their $1 a gallon sale yesterday so maybe you can drop 20$ and pick up a 20 L tank or a 29g. Give the fish more room since they are gonna be in there for awhile. But also keep in mind the larger the qt the more meds you have to administer and control.