Your slide tabs are drag n' drop enabled, you can grab any and reorder them as you like.
Since LayerSlider WP version 4.0.0, there are more than 200 built-in preset slide transitions.
If you create a new slider, the new slide transition will be used by default, but you can still
use the old one with the switch in the slide options.
You can choose transitions you like with the "Select transitions" button. If you choose more than one transition, LayerSlider will use a random one from your selection. If you don't choose any of them, a random one from all the available transitions will be used.
Please note that you have to save your slider after selecting new slide transitions.
Easings are timing functions of the animations, you can manipulate the objects movement with it. Please visit this page to find out more about easings and see real-time examples.