Coveted Jewel's last ability triggers after you declare blockers (or declare no blockers at all) if any attacking creatures are unblocked. It doesn't matter if some attacking creatures were blocked.

A creature attacking a planeswalker you control won't cause Coveted Jewel's last ability to trigger.

Coveted Jewel's last ability resolves after blockers are chosen but before combat damage is dealt.

If more than one opponent attacks you at the same time, Coveted Jewel's last ability triggers for each of them. You choose which player ends up with Coveted Jewel, but each of them draws three cards and has a chance to activate its mana ability.