I think you are talking about physically sizing the separator as opposed to mechanically designing the pressure vessel. If that is the case, I suggest you look at the GPSA Engineering data book under the section on separation. API 12J is for oilfield gas/oil separators but the sizing concepts in Annex C would be useful to review. I'm not aware of any code like the ASME section 8 Div 1 if that is what you meant by Code.
Theoretically, there is no reason that you can't separate out physical particles from a gas stream in a separator the same way you do liquid droplets. In both cases, you are going to need to know the physical properties and the size of particles you want to remove, below a certain diameter the particles' settling velocity just become too low to practically settle them out using gravity. You might be better off with a physical filter to remove dust.
Pressure drop in a scrubber, too many variables. If you are talking about a conventional 2 phase separator with or without a demister pad you are talking a few inches of water typically (you can calculate it, you have an inlet and exit loss plus the pressure drop across the demister pad or other internals if you chose to install them). For a physical filter, the pressure drop is likely to be quite a bit higher. You can size a filter for whatever pressure drop you want but the lower the pressure drop, the more filter elements you need and therefore the higher the cost.
