The cold at night is likely effecting the uptake of certain nutrients, calcium be one of them. Day time temps are good and I saw you post the Rh, which looks good as well. You'll definitely want to water to run-off, about 10-20%. Don't let your plant sit and soak in it. If you have racks, you can let it drip down into a pan, if not, you can collect the run-off water with a turkey baster from the pot saucer.
For now, try and find a way to bring those night temps up to 65 if you can. I have a little space heater that keeps mine warm. Bought it at Target for $15. The spots I see in the new picture you posted, do look like a calcium deficiency to me, but the temp needs to be corrected for the best results when trying to correct the issue. Its not that the soil doesn't have it, the calcium just isn't in available form right now for the roots to take it up.