Here’s my WAG from the other side of the internet. (it’s kinds hard to see your plumbing from here) Perhaps the dryer vent is warming up the air around the pipes. Warm, moist air will condense on cold water pipes. I doubt it has anything to do with direct contact. Insulating the pipes should help. Also, if the dryer vent is leaking it will be leaking very warm moist air.
As far as your leak at the shut off valve, I am not fond of the theory. The ‘adhesive’ (whether it is pipe dope or solvent cement) should not be affected by warmth. On the other hand, PVC is not designed for hot water and it gets soft when heated. If it is getting really warm and it is a threaded PVC connection, the threaded PVC could be getting soft and causing the leak.