Definitely let them sit open for a while so the chlorine can evaporate. Tap the jug so the air bubbles all come to the top.
TSD is checked with a meter that looks just like a PH meter. Good to know if you can spend the $15-$20. My tap is 164ppm which I think is high but I’ve seen others way above that. When I switched from distilled to tap I got a little tip burning. Hasn’t spread so I’m not concerned but I’m guessing it’s my tap water.