Premiere Pro 5.5 and earlier can't apply effects across clips. CS6 will add a new capability, adjustment layers, just like in After Effects or Photoshop. This will allow what you desire.
For now, it's one clip at a time.
You can also apply effects to a nest of clips.
Good point. Forgot about that.
I'm running Premiere Pro 5.5 and have been able to lasso and apply my effects to several of my clips all at once.
Once you apply the effect and fine-tune (if need be), you can right-click and create a User Preset to help save time (say if all of your clips needed to be color corrected). The User Presets are the first folder listed in the Effects bin.
As far as the effects order are concerned, you pretty much have to play around with those yourself. I use a Video Limiter effect with a ProcAmp and have noticed that if they aren't in a certain order (the first listed effect is the first applied...) it changes how it looks and not always for the best. Best bet is to play around and see what order of video effects works best for you.
On a related topic, does Premiere apply effects in a chain, as they are added, or does it automatically perform an reffect first if it should be applied first? In other words, does it matter in what order the effects are applied, and if so, is there a rough order of how they should be applied?
Yes, but you can change the effect order by dragging the effect name in the Effects panel. They render from top down.