Hello Mati!
You can preview multiple animations at the same time using the Preview View:
Preview - Spine User Guide
You can't set a delay, but you could set the speed to 0, then add all of the animations, then reset the speed to normal.
If two animations don't have the same lenght, each will loop on its own time without waiting for the other to end.
There are improvements planned for this view:
Preview view improvements · #371 · EsotericSoftware/spine-editor
You can't edit multiple animations at the same time or preview them outside of the preview view, but you can keep the view open both in setup or animate mode which is pretty handy.
If you find that your dopesheet is hard to read, consider trying to use filters or lock your dopesheet on the elements relevant for you at the moment:
Dopesheet - Spine User Guide