Hi,
ad 1) It can be done only via Custom CSS. Example CSS that you can use, and will hide dots:
@media screen and (max-width: 680px) {
.sp-slider .sp-dots {z-index: -1; display: none; visibility: hidden;}
}
You can use it inside Page Settings > Page CSS > Custom CSS area (for that page only)
OR for whole website: in Template Options > Custom Code > Custom CSS or inside custom.css file
ad 2) I have to see website URL with that slideshow to tell more.
As alternative way, you can prepare slideshow addon only for Mobile view, with smaller resized images. Addons settings allows you to control when addon is displayed, use : Advaced (tab) > Responsive - Hide/Show