Should you wash raspberries?
Like anything else food-related it's a matter of risk. If I'm picking raspberries straight off of my bush I often eat them without washing, but if I have a lot of them from the store I wash them as I don't know what they have been exposed to in packing and transit. Many people do not do this and get away with it just fine, occasionally someone gets sick. How much of a risk it is depends on the source of the berries, how they are packed, etc. and most of the time this is a complete unknown.
As for how to clean them it's important to be gentle, especially with very ripe raspberries as they can easily break apart. It's similar with blackberries, when I collect wild berries I accept that I will lose 5-10% of them in washing as some of them simply dissolve for lack of a better word. I minimize this by gently filling the container with water, soaking then for a few minutes, agitating them gently with my hand, then draining them. If they are good and solid you don't have to be this careful.
Raspberries don't absorb water, it's the cavity that gets filled up that gives that impression, so to drain them effectively I tilt them in all directions, letting the water run out no matter the orientation of each berry.