Wiring – How to wire GFCI together with two switches controlling light/exhaust fan and vanity light

This is a bit more annoying than it looks (spoiler: the obvious way to wire it may not pass muster with all inspectors)

The power feed to this all comes in at box 1 (vanity light) and feeds the /2 switch loop to box 3 as well as the /2 feed to box 2. Box 2 and Box 3 are connected by a /3 cable, apparently intended to be a switch loop.

With all this, you'd think you'd be able to:

1. Turn the power off, of course
2. Connect the white wire from the /2 in box 2 to the white wires from the light and fan there.
3. Connect all grounds together in box 2 and to a box ground pigtail (if it's a metal box)
4. Connect the black wire from the /2 cable in box 2 to the white wire in the /3 cable and mark that white wire as a hot (permanent marker as you have done should be fine -- it just needs to be a permanent/indelible marking, visible from all angles).
5. Connect the red wire from the /3 cable in box 2 to the blue wire from the overhead light.
6. Connect the black wire from the /3 cable in box 2 to the black wire from the bath fan.
7. Connect all the grounds in box 3 together.
8. Connect the white wire from the /3 cable in box 3 to the HOT terminal on the fan controller after marking it as a hot.
9. Connect the black wire from the /3 cable in box 3 to the 1-POLE terminal on the fan controller.
10. Connect the white wire from the /2 cable in box 3 to the switch HOT terminal, again after marking it hot.
11. Connect the black wire from the /2 cable in box 3 to the switch 1-POLE terminal.
12. Connect the red wire from the /3 cable in box 3 to the other switch 1-pole terminal -- the Adorne parts can terminate two wires on each terminal.
13. Button everything back up and turn the power on.

and have it work. In fact, it will work if you do this; however, there's a catch! This arrangement takes one switch loop feed (from the vanity light) and returns it back down two different cables (to the vanity light and to the overhead light), which can be seen as a Code violation (of the 300.3(B)/310.10(H)/300.20 complex) as it creates a large loop area that puts out stray magnetic fields in your bathroom (good for ruining the picture on that old TV you have mounted in the wall in there ;).

A more conservative approach would be to utilize a dual pole switch to break the two hot feeds simultaneously while sending the return paths back the way they came, as follows:

7. Connect all the grounds in box 3 together, and to grounding (green/bare) pigtails to any switches that need them.
8. Connect the white wire from the /3 cable in box 3 to two (preferably black) pigtails after marking it as a hot. One pigtail goes to the HOT terminal on the fan controller and the other goes to one side of the dual pole switch.
9. Connect the black wire from the /3 cable in box 3 to the 1-POLE terminal on the fan controller.
10. Connect the red wire from the /3 cable in box 3 to the other terminal on the same side of the dual pole switch as the pigtail.
11. Connect the black wire from the /2 cable in box 3 to the other side of the dual pole switch.
12. Connect the white wire from the /2 cable in box 3 to the other terminal on the other side of the dual pole switch.
13. Button everything back up and turn the power on.

This arrangement also works, and keeps the two light switch loops neatly separated. However, Legrand does not make a two pole Adorne switch, and I do not believe there are faceplates available for the combination of an Adorne device side by side with a standard switch in a two gang box. You'd have to get a standard-form-factor (i.e. not Adorne) fan controller to do this.

The two-way switch in the picture switches a single conductor on and off. I expect you will find that the switched black wire and a neutral white wire lead up to the ceiling fixture. With this setup it's not possible to separately control the ceiling fan and light. But it should be possible to turn them both on and off together. It sounds like that's what you're trying to do.

The exhaust fan should have come with some instructions on how to wire it. We expect to find a neutral white wire, two hot wires (black and blue?) and a grounding wire (green or bare). If the existing wiring to the ceiling is non-metallic cable then you connect black to black/blue, white to white, and green to green/bare or grounding screw. If the existing wires are run as metallic shielded cable then the shield provides grounding and you will need to bond the grounding wire of the fixture to the metal ceiling box.

It sounds like you've attempted the first scenario but the fan is not switching on? Some bathroom exhaust fans are setup to run for a fixed period of time after detecting a certain level of humidity. These can be finicky and may not always turn on when switched on. You might read over the instructions to see if this is what's getting in the way. If it's a simple fan + light then tying the hot wires together should cause them both to turn on. Check your connections and if you can't get it to work try connecting one at a time to debug. It's possible the fan is a dud out of the box.