I only need a single pole dimmer switch. Which product do i buy. I bought the smart dimmer system remote, but it doesn't seem to be right.

Single pole switch?
http://waterheatertimer.org/How-to-wire-switches.html

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Usually this is indicative that you have a 3-way lighting circuit, but only a single-pole dimmer. For most lighting circuits, the red wire and one of the black wires are supposed to be run over to a second light switch. You need dimmer rated as a "3-way" in order for that to work. If you get stuck, I would call the manufacturer's tech support number at 1-800-523-9466. They're available 24/7 and it will not cost you anything.

One of the blacks is a hot that connects to the black wire on the switch. The other black wire is the switch leg (to the light) that connects to the blue wire. The yellow wire on the switch is not connected in a single pole application. If you don't know which black wire is hot you'll need a volt tester.

The CA3000 is then controlled with the CA5500BR Handheld Remote with Smart Base.
http://fmal.info/intermatic-ca5500br-intouch-wireless-hand-held-remote-controller-and-smartbase-kit

I don't think you can do what you are trying. The fan & light are on one circuit. Probably, originally, there was only a light fixture there. The fan/light is on a single circuit and the remote does the controlling of both units.
Now, you are trying to install a fan control and light dimmer but you don't have wiring for each separately.
You might be able to use one of the dimmer controls to adjust the output to the fan/light combination, but you can't control them individually, if I understand your wiring.
Gary

The question is unclear.
Switches are single-pole or 3-way.
Single pole switches have 2 screws plus green ground screw.
3-way have 3 screws plus green ground screw.
I don't see Lutron rania dimmer
http://www.lutron.com/Products/StandAloneControls/Dimmers-Switches/Pages/DimmersSwitches.aspx

Identify your switch and your dimmer and add a comment.
I will look up the information.

The problem is most likely not the dimmer or the wiring, but rather the existing 3-way switch.

First of all, the Aspire smart dimmer does not work in conjunction with traditional, 3-way, on/off toggle switches. When the 3-way switch is in one-position, it lets the dimmer work, but in the other position, it cuts power to the entire lighting circuit - and the smart dimmer is NOT going to be able to override that. You instead need to get the corresponding remote dimmer (sometimes called a slave, or a companion dimmer), and use that to replace the standard 3-way switch.

That may also solve your "mystery turn-on" issue. Even though those dimmers can use the existing 3-way switch wiring, you have to REALLY pay attention to the instruction sheets to see how the master and the slave wire up to each individual electrical box. I vaguely remember that even if you were to use the product in a single-pole application, those two wires that, I assume, you attached to the traveller wires in the house needed to be shorted together in order to work - and since you have them running into a 3-way switch, the errors that you're seeing are bound to happen.

Long story short, get the slave dimmer, install it according to the instructions, and all these problems should go away.

The problem is that the Cooper #9530DS-K-L is actually a 3-way switch and you need a single pole dimmer switch to replace your existing single pole toggle switch.

If you want to use the Cooper switch you have you can take one of the black wires and cap it with a wire nut and connect the other two wires, but frankly, you'd be paying about 2 times the price for a 3-way dimmer switch when you only need a single pole switch.

You should be able to return the switch and get the correct one.

You should only have (2) black wires on the proper replacement switch, plus a ground wire

Hope you found this very helpful and best regards!

The old switch is just a single pole switch. The new one is for fan speed control. You need to use a regular single pole switch like you had. Or you can use a single pole switch on the Lutron you bought if you can figure out which wires to use. Do you have a meter?

If you need further help, I’m available over the phone at https://www.6ya.com/expert/craig_3fa289bf857b1a3c

Home Depot sells Lutron dimmers which are single pole and basic.. www.homedepot.com