Hi - Quick question: In order to play cards like "Sith Library", do I have to have an objective card with "Coruscant" in play (ie, to have the "relevant" location available)? Otherwise, why is there this location on the card?

All you need is the resource match. The location only comes into play if you have a card ability that references a location. You might have an ability that says cards with location x cannot be targeted by an opponents event cards.

Yep, traits have no inherent gameplay effect but can be referenced by other card effects. Sometimes, may just be for flavor.