Bathroom exhaust fan wiring
Currently it appears you have 2 switches Providing power to the location and 3 loads,
On the fan. Normally all the whites go to the white,
the green and bare copper wires are connected ground there should be one or the other or a green ground screw to land the ground on.
Next try putting black with black red with red and leave blue disconnected to test.
Did the light come on with 1 switch and the fan with the other? Make note of what happened.
I usually connect the fan and light together on 1 switch if they are the ones that came on turn the power off again put them both on the same switch.
Now put blue on the other switch. Now when you are in the bath the light and fan will be on and only when you want heat turn the other switch on.
If this is a different setup possibly a timer or humidistat we might need to make more changes to the wiring but for a light, fan and heater this wiring would be normal with 2 switches.