追 as in 追剧 (chasing a TV series) I am native speaker but I haven't yet figured out the exact meaning of 追 as in 追剧 - 'chasing a TV series'. Does it mean 'stay on top', 'catch up' or simply 'actively watch'? In other words,


Does it exclusively refer to watching the latest episode on air, or at least keep oneself up to the season? 
Does it count as 追 if I am watching the past season on DVD in order to catch up and watch the current season? 
Does it count as 追 if I am watching a series that has already finished?
Yes. This is exactly what 追剧 mean.
No.
No.


We may call actions in last two question as 煲剧 or 补番 .

EDIT:

There is a funny name 坑 (means 'hole') for the series that have many seasons to watch. When we start watching it, we call it 开坑 (start a hole), and the process we watch from the S01E01 to the latest episode, we call it 填坑 (filling the hole).
That a funny saying we are using.