Hi, I've just been getting into dramas recently and I noticed a trend where there would always be a subplot of sorts with a main antagonist present. The antagonist would always seem to scheming to make the other characters' lives miserable or just manipulate them for their own gains. I wonder if there are any dramas that doesn't involve such a character, the protagonists could be up against an organisation instead of a single character for instance. Would love to watch some light-hearted drama. It would also be great to have recommendations for dramas that have less than 20 episodes!

School dramas are great for not having a single antagonist! I particularly enjoyed School 2013, Reply 1997, Reply 1994, they are also very light hearted. 

There are also some gender-swap dramas like Sungkyunkwan Scandal or Coffee Prince which are very light hearted. 

If you are looking for something where the protagonists are up against an organisation the best example I can think of is Doctor Stranger. Angry Mom also has some elements of the bad guys being in an organisation, but there are characters in there which I completely hated. Healer also kind of fits this bill of being up against an organisation but I found it far from light-hearted (it is very good, but quite action-packed). 

Sorry to be making all sorts of random suggestions, I tried to take a look at your list to get a feel of the sorts of things you liked but there isn't much on there yet.

Watch kill me heal me!!! Its awesome!  Playful kiss , My princess , You're beautiful , Goong , heartstrings ,.. 
Watch Noble, My Love. No antagonist there. Each episode is only 15 minutes.
Secret Garden didn't really have a main antagonist. 

Same goes for The Master's Sun and It's Okay, That's Love.  

Jdrama there is Nobunaga's Concerto and Dear Sister.