The definition
System factor: most correlations are established for standart systems (hydrocarbons). Some systems can be foaming, ... and will call for some derating. The system factor is a coefficient applied for such cases. Is often equal to 1.
%Jet flood Jet flooding occurs when entrainement is so high that liquid reaches the next tray. The point at which this appears is the jet flood point. The %jet flood is just how close you are from this point. At 100% the column is flooded and cannot be operated.
%Downcomer flooding
When the liquid rate is so high that the downcomer cannot evacuate the liquids from the tray to the tray below, It floods. The %Downcomer flood tells you how close you are from this point
Jet Flooding is mostly related to vapor rate, Downcomer floodind is related to liquid rate. The higher the pressure, the more concerned you should be with downcomers, because the volumetric L/G increases.
Downcomer backup: more or less the level difference between the liquid level on the tray, and the liquid level in the downcomer. This is important to prevent vapors from going through the downcomer.
Turndown: Maximum rate/Minimum rate at which the column operates properly. Should be as high as possible, but be careful if you see figures greater than 2.5 (for trays). It's a ratio maximum to minimum
Maximum pressure drop: probably the total pressure drop at maximum rate. You are correct, this is a kind of measure of resistance of the colmun to the flows.
Maximum dry pressure drop: Probably the pressure drop at maximum vapor rate, when no liquid (or no reflux) if fed to the column. Not the same at the one above . In my own opinion, of little use.