Can dust cause damage to my motherboard?

Dust is a problem from the standpoint of blocking fan vents, or, if deep enough, actually insulating parts, causing overheating, but unless it contains substantial amounts of corrosive or conductive material (in which case you shouldn't be breathing it), it won't damage the electrical components (beyond any overheating damage).

What could happen, in some circumstances, is condensation inside the box, mixing with dust and creating a conductive sludge. This would generally only occur if you bring the box in from an extremely cold environment (below 0C, roughly) into a humid indoor environment. The protection from this is to wrap the box tightly in plastic before bringing it indoors, and leave it wrapped for a couple of hours, while it has time to warm up.

No way. Unless it over heats. Trust me, I have cleaned server motherboards deployed in Afghanistan for months with inches of dust caked on, still running fine. And as long as you keep them cool, they will survive.

Now, optical drives. That's a different story.

It hardly will cause short circuits, but it definitely leads to overheating. Your screen frozes are the consequences of this. You should clean everything with dry soft brush. Also check that all coolers are rotating. The speed of CPU fan you can see in BIOS/Power Management. Optionally you can see there the speed of other fans if they do support the feature.