Household appliances commercial project EU certification
The detailed technical information on your product would be needed to advise on exactly what standards may or may not be applicable. But I can talk in general terms.

I know that the necessery things to do are: certification EMC, RED,
LVD...

This is not anywhere near as simple, you also need to declare compliance with the correct parts of each. For example, you cannot declare compliance with the safety parts of the LVD if you need to declare compliance with RED.
I would strongly advise getting consultancy from a test house (or a dedicated compliance consultant), they are usually very helpful.
I would also look at the Declarations of Conformity from other similar products already in the market. This will give you an idea of what standards you may have have to declare conformity against (a test house will always tell you that what you need is more tests, having an idea of what may possibly be required will allow you to ask intelligent questions).

Are making the tests obligatory for the norms? Or only the producer
statement is enough to let the product enter the market?

Technically, yes. You can self-declare compliance with only a Technical File.
I can't emphasise enough that I think this would be an extremely bad idea, as you don't seem to have the knowledge required.
One of the possible things that can happen if you are found to be non-compliant in the market is forcible recall from customers at your cost. These regulations have teeth and can bankrupt companies.

whether the certification of my own remote controller with
precertified module on my own PCB circuit with battery (CR2032 3V3)
supply and 4 buttons is as expensive as using a not precertified radio
module?

It should be the same price, the same tests need to be made. The advantage is that you have a good chance of passing emissions with a pre-certified module. It is one less, major, uncertainty in your compliance process.