What is usually called paint thinner is mineral spirits. There is some stuff called low odor paint thinner I've never found any use for especially thinning paint. The best thing to do when using any paint is not play chemist. Use the solvent recommended by the manufacturer, their brand. Reducers are a mixture of a lot of different solvents designed to go with a particular paint. Normally using an oil based paint it is recommended to use naphtha for paint to be sprayed. Look for that recommendation on the can.
As far as cleaning the parts it would depend on what condition their in. If they are relatively clean and rust free just use a wax and grease remover. If they are rusty or has flaking paint, it would be best to sandblast them to bare metal.
If they are caked with grease wash with oven cleaner. Note: if you use oven cleaner after you rinse treat with vinegar to neutralize the sodium hydroxide.