Hi, I’ve created a character using linked skeletons and images, now I want to create various animation of the same character such as walking, running and jumping.
What’s the best way to do this? As in, is there a way to make the character shared between different animations so that, for example, if I change the color of the cloth, all animations get updated at the same time?
And what if I want to re-use the same animations for different characters by replacing the images?
Hi and welcome here 
In Synfig, imports are done by “including” on-the-fly.
So what you can do is to use a base character animation and duplicate it according your needs.
Most of the time you will have to replace the images (and readjust the joints points of the character, if not exactly the same shapes.
For changing the colors or the clothes, it will be the same.
But in that case you can also include several variation of the clothes in the same animation and select which ones to be displayed (with a switch layer or changing the opacity).
A last possibility about the color is to change it directly, but it has to be made in vectorial.
Why not a layer above the clothes with a selectable color? 