If Skyclave Shadowcat has a +1/+1 counter on it and it dies, its last ability triggers.

If Skyclave Shadowcat dies at the same time as another creature you control with a +1/+1 counter on it, its last ability triggers for that creature.

You draw just one card each time Skyclave Shadowcat’s last ability resolves, no matter how many +1/+1 counters the creature had on it.

If a creature with a +1/+1 counter on it died due to receiving too many -1/-1 counters, it dies at the same time that the counters are removed, and Skyclave Shadowcat’s last ability triggers.