追 as in 追剧 (chasing a TV series)
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.