Just two questions

1) Can I attack an objective if none of my ready units can deal objective damage?

2) Can I attack an objective if my opponent doesn't have any defenders, or does that just count as one unopposed damage against an objective?

1) Yes.

2) Yes and you will get unopposed bonus damage at the end of the engagement.

It's fun to attack an enemy objective with just a Repair Droid.

It's fun to attack an enemy objective with just a Repair Droid.

or C-3PO

I was laying the beats down with some Jawas the other day. Not entirely proud of it myself, but was amusing none the less.