Your wiring looks okay (except for the redundant "power to dimmer" and "power to fan" wires -- as I commented, you don't need the extra pigtails, just connect the switches directly with one marette).
I can think of 3 possibilities:
- The z-wave dimmer is not operating properly with the CFL. Try using a regular incandescent or halogen bulb, and see if the problem goes away.
- The z-wave dimmer is being affected by the electrical/RF noise that the fan generates when it turns on. Ensure the fan switch is designed to handle inductive loads, or try replacing it with another brand of switch.
- The z-wave dimmer is defective.
OK, this is kind of a rambling question with a lot of details, but let me give you some leads on some of them:
Wall Plate
If you want to install a wall plate, you'll want to clean up the opening and then install a "low voltage mounting bracket", which is a square piece of plastic that frames the opening and provides a place to attach the plate:
(Wall plates come in sizes like 1-gang, 2-gang, etc., which indicates how many toggle switches or receptacles it can fit. You might want a 2-gang for that size opening and number of cables).
Then you can get a "keystone plate", which is a wall plate with small square holes in it (available in various widths and with different number of keystone holes). Here's a 1-gang, 2-keystone plate:
Finally, you get different keystone modules for the different types of cables. They snap into the holes in the plate. This lets you mix and match different connection types on the same plate. I'm not really sure what you mean by "tv type" and "telephone type", but here's a coax keystone module:
(EDIT: resist the temptation to skip the bracket and screw the plate directly to the wall. The screws will pull out of the drywall in about 2 seconds. I've seen this happen in several houses where people added coax wall plates or something, and didn't bother to do it right.)
Shelf & Mounting
As for wall-mounting options, it depends on how tidy you want to be. You could either mount a small shelf to the wall and place the electronics on that, or use your pegboard and find a way to strap the items to it.
Personally I would mount the shelf or pegboard just below the wiring plate, not on top of it. That would make it easier to mount the wall plate, and easier to make changes in the future.
Whatever you mount to the wall, make sure you attach it to the studs behind, not just screwing into the drywall.
Best Answer
This is an old question, but there are several solutions here that may help others who stumble upon it.
The easiest and most consumer-friendly way to do this is with a "smart" thermostat, these are designed to be controlled remotely and also can be activated when you're home/away, at a set time of day, minimum/maximum temperature, or when you reach a certain distance from your house (tracked by GPS).
The Sonoff you mentioned is capable of doing this as well, in a tinker/hacker way. I would actually recommend you use a 2-channel Sonoff so one channel can control heating and one channel control cooling. As you're configuring the Sonoff remember that "inching" means "momentary connection" and "locking" means "closed circuit" like a normal switch. I believe thermostats "lock" until the desired temperature is reached. Sonoffs contain relays with several hundred volts and several amps of capacity.
As @dandavis commented previously, I would wire these in parallel with your thermostat wiring so that your thermostat still controls your system also. The answers about what to connect with what should be in your thermostat manual, I haven't read it. If you're more of a "do-er" than a reader, you can use a voltmeter to check the thermostat's continuity during operation and figure out where to bridge your Sonoff that way.