Sometimes requires more than one application, but yes, it does work.
Epsom salt is magnesium, an essential plant nutrient, so I doubt this would work. I use table salt. & it can be any brand of detergent, it just serves as a surfactant so it doesn't roll off the plant, & it helps it soak into the soil. It will kill most weeds, at least the tops, but you have to drench them all through the root zone to have any chance of real eradication. It isn't systemic the way Roundup is--it has to contact all the parts of the plant. Don't use it where you want anything else to grow, but it's good for weeds that are coming up through cracks in the pavement or a gravel path. Boiling water is also good in those situations.
(I have a degree in horticulture.)
Thank you!