What you propose is indeed possible. How difficult it is, depends on what wiring is currently in place.
You should start by connecting all the bare/green grounding conductors in the switch box together, including a pigtail to both switches. Other than that, it sounds like the wiring in the switch box is good to go.
If you want to control the fan with a wall fan control, you can install that in place of the fan toggle switch.
In the ceiling box, you'll likely find the 12/3 cable from the switch box. If the existing fixture uses a remote module, you'll likely find that either the black or red wire from the 12/3 cable is simply capped off. You'll see the black/red, white and ground wire connect to the remote module. The remote module should connect to the fixture with a black, blue, white, and bare/green wire.
If you want to remove the remote module, you should disconnect it from all the wiring. Once disconnected, you can remove the module, or cap off all the wires and leave the module in place.
To control the fan using only the wall switches.
- Connect the white wire from the ceiling to the white wire from the fixture.
- Connect the bare/green wire from the ceiling to the bare/green wire from the fixture. If the box is metal, include a pigtail to the box.
- Connect the red wire from the ceiling to the blue wire from the fixture.
- Connect the black wire from the ceiling to the black wire from the fixture.
Now the switch connected to the red wire, should turn the light on/off. The switch connected to the black wire, should turn the fan on/off (and optionally adjust the speed).
This, thankfully, is simple. The black wire in that outgoing cable to the fan connects to the fan and the red wire connects to the light -- so you simply have to pigtail the black and red wires together with a wirenut and a short length of wire, and connect the pigtail to the switch terminal. That will give you simultaneous control over the light and fan from that switch, while leaving your options open to install a double switch or fan controller later.
Best Answer
First off, the two neutral wires in the back of the box provide the path back to the source for the current that powers your fan, so they need to stay nutted together or else the fan won't work.
The ground wires should be terminated to the box, though. Some boxes are functionally grounded (via conduit or cable armor) even if there is no ground wire present, and I can't tell if yours are that way or not from here.