Mainmenu and logo disappreared on mobiles.

You can change the media queries at the file:
modules\mod_slitslider\assets\css\ responsive.css

I changed this file exactly as you said, but you can check on the URL I sent that it doesn't make the slider responsive.
Clead cache and tested on 2 computers.

And what do you mean with "not responsive"

Just the same thing as everybody, I think : the images are not resized on small screens, so, on mobile phones for ex., we can see only a small part of them.

Yes, because it makes no sense to show a big images on mobile devices.
But you can show a bigger part of the images, if you change the "responsive.css" like this:

@media screen and (max-width: 1000px) {

.jpslitslider .sl-slider-wrapper {
height: auto !important
max-height: 100% !important;
}

.jpslitslider .sl-slider p {
font-size: 12px!important;

}

}

it makes no sense to show a big images on mobile devices

This is your opinion.
I need this slideshow with the titles on mobiles (... and it makes sense )

If your component Slitslider is not responsive, I have to install another one.