Are these relays connected correctly? I currently have limited electronics experience. I am planning to use mains power through relays for climate control, so considering the risk, I would like to check to see if these relays are appropriately connected to receive mains power.

I have two relays. One relay will take 600W (a heater) while the other will have 50W/0.2A (a fan). 

The relay module is: https://www.auselectronicsdirect.com.au/assets/files/(ST1080)5V%20Relay%20module.pdf
There seems to be a resistor inbuilt into the casing, and according to the packet (but not the PDF) there is inbuilt Back-EMF protection. 

My concern is that it may not be protected against inrush, uses screw terminals, and may not be isolated.

Diagram is:


Any advice will be appreciated. Once again, I will not run mains power through it until I am sure of it being safe.
Yes, your relays are hooked up the right way. I'm using the same modukes to drive a fan 75W and a HPS-Lamp with 400W. As long as you drive the heater with AC voltage, you're in the specs (different than stated in previous comments).
But the humidity sensor (a DHT11/22) isn't, as far as I remember its pinout...
And could you explain what the Transistor is for (if it is a transistor, I'm curious what you want to achieve with this wiring)?