Regular Dimmer will work.
In most cases, it is possible to install a dimmer switch or rheostat on a halogen light fixture. However, it is important to ensure that the dimmer is compatible with the specific type of halogen bulbs being used. Some halogen bulbs require a specific type of dimmer switch, so it is advisable to consult with the manufacturer or an electrician to ensure compatibility and safety.
It was not designed to be used with a dimmer switch. You must have a halogen designed for use with a dimmer or it will not work.
Yes. There are various types of dimmers. Look for the halogen dimmer in your favorite search engine.
because of voltage
You cannot use most fluorescent lights with a dimmer. Just about any incandescent bulb WILL work with a dimmer. Occasionally, when a halogen bulb burns out, it will destroy a dimmer switch but halogen bulbs are considered incandescent and other than that little problem they work well with a dimmer.
Halogen is a type of incandescent fixture so yes.
Although a dimmer can be designed for 12 v halogen lamps it is more common for dimmers to work on higher voltages. Dimmers have to work into a resistive load so it is not usually possible to place the dimmer on the high-voltage side of the 12 v transformer that comes with the lights.
something in a circuit
Dim lights are almost always a bad ground connection on the dim light, just loosen and retighten the ground wire to restore the connection.
Halogen lamps should not be dimmed. At lower voltages the halide is not hot enough and will condense on the glass bulb, darkening it. You will be replacing bulbs all the time.
It is very simple to install a dimmer switch in place of a regular light switch.
I think the term you're looking for is "regular variable."