I guess by "swapping" you mean you want to stop playing one animation and play another on track 0? Sure, just use AnimationState setAnimation with zero mix duration.

What do you mean "syncing time"? You can set TrackEntry trackTime to start an animation at a specific time. For example, among many other scenarios, this can be useful when changing from run to walk so the feet transition smoothly. If the foot is forward in the run animation, but you start playing run while the walk animation has the foot back, it can cause an odd stutter step. You can set the trackTime of the run animation TrackEntry based on the trackTime or TrackEntry animationTime of the walk animation.

Yes.
Animations are played in a Spine AnimationState in TrackEntry objects.

When you call SetAnimation, it returns a TrackEntry for that animation you played.
Get that TrackEntry's TrackTime and keep it in your class.

Then when you call SetAnimation for your next animation, also set the TrackTime of that new TrackEntry.

var walkEntry = animationState.SetAnimation(0, walk, true);

//... then later

float walkTime = walkEntry.TrackTime;
var runEntry = animationState.SetAnimation(0, run, true);
runEntry.TrackTime = walkTime;