Can I have analytics/click tracking on the slides/links?

Smart Slider 3 does not have an option for this. Most click trackers work that way, that analytics codes are storing the visited page's url, so it is not the source of the link they are storing but the visited page. You could try to use custom codes, but please note, that we do not support custom coding, so you have to write the entire code yourself.

Google Tag Manager

Google Tag Manager only sees links which are using a tags. Layers, like the Button, Heading or Image layer uses those kind of links.

It doesn't see JavaScript links, which are used by container elements, like the Slide, Row or Column.

But Google Tag Manager offers an option to track clicking on any element of your website. So you can track any element's clicking, even on a slider, but you will need developer knowledge for this.