Just finished all 25 episodes of this series. A very Delta/Fi-centric show, I thought. Here are my impressions of the characters/actors:
Geum Jan Di (Ku Hye Sun) - Delta NF - EII? I'm thinking her behavior demonstrated a lot of Se-POLR. No doubt she was Fi-dom. And very infantile. VERY.
Goo Joon Pyo (Lee Min Ho) - LSE; I think he was functioning in his Id before he met Jan Di, because of his anger and social isolation, which made him seem SLE at first. However, he responded extremely well to "lessons" in Fi from Jan Di and fell in love with her in the process, which makes him LSE. (I think he's an ST, not LIE, but I could be convinced otherwise, seemed to be a caregiver too). Previous to meeting Jan Di, he did get Fi to some extent from his F4 friends and sister, but not dominant Fi.
Yoon Ji Hoo (Kim Hyun Joong) - Si-dom or EII or Ni-dom. He was one of the harder ones for me to type. At first he seemed Ni-dom in a way, because of his apparent dreaminess and almost seeming psychic in terms of being where Jan Di needed him, in just the nick of time. However, it became apparent later that often Ji Hoo would appear places because Joon Pyo would send him a text to go rescue her whenever he was in trouble. Ji Hoo's dreaminess also later seemed retrospectively to be possibly Fi-motivated wistfulness about his love (for Seo Hyun initially; for Jan Di later) and guilt about his family's accident. Instead he seemed more stoic than dreamy, and demonstrated himself to be very focused on caregiving. An alternative typing besides SLI might be Jan Di's identical EII. They even have similar demeanors (except Jan Di is much more clumsy) and smiles. I could also see Ji Hoo possibly being Joon Pyo's dual, though wouldn't explain why Joon Pyo was so undualized initially. His demeanor just seems much more refined compared to what i think of with SLIs (contrast, his grandpa who i think is Te-SLI). Maybe he was ILI? I guess Ji Hoo is just all types rolled into one... I felt like he was portrayed as the epitome of perfection on the show.
So Yi Jung (Kim Bum) - IEE. OK this is in part because I've seen him typed IEE in Eunice's Asian typelist thread, but i stuck with it because it didn't see a reason he couldn't be. He does have that typical IEE smile, and he'd been a big Don Juan type before he got over his unrequited love for Eun Jae and fell in love with Gaeul (his identical)
Song Woo Bin (Kim Joon) - Ne-IEE. Looks it (he reminded me of Ssmall actually ), and was reputed to be a "Casanova" with women (i guess stereotypical for for male IEEs).
Chu Gaeul (Kim So Eun) - Fi-IEE? delta NF for sure. Her demeanor just reminded me a LOT of myself.
Joon Pyo's mother (Lee Hye Yeong) - SLE. Obsessively power-focused, absolutely ruthless. The benchmark SLE if there ever was one.
Joon Pyo's sister (Kim Hyun Joo) - SEE maybe? she has an easier time standing up to and influencing the mother than the others. Proficient in Fi and highly valuing of it.
Ha Jae Kyung (Joon Pyo's "fiancee") (Lee Min Jeong) - SEE or LSE. SEE I think, just based on the way she approached trying to make Joon Pyo like her (a little aggressive). Alternatively, she may have been Joon Pyo's identical (LSE)... they seemed to have eerily similar thought processes and ideas (the J J tokens, the watching the horror movie, etc). She approached wooing Joon Pyo by trying to be his caregiver, which he really didn't care for.
Sunny, Ginger, Miranda (mean girls clique) - betas (the leader is SLE i'm pretty sure)
Ji Hoo's grandfather (the former president of Korea) - Te-SLI?
Jan Di's parents & little bro - alphas? WAYYY too hyper.