Sorry for the late reply, I ended up asking my cousin some of the questions to get a more native korean answer to some of them and I’ve included some links as obviously I’m only one person and I’ve lived in the UK for most of my life, so feel a bit bad answering on behalf of the whole country lol! And obviously varies from family to family, this is just my take on it all!
-Extremely pushy mothers and their relentless quest to marry off their children to other families with an appropriately high social standing (with the fathers seemingly having no skin in the game)
Korean parents for the most part are incredibly pushy, not just with marrying off but in every area of your life, for example in education, cram schools that go late into the night are insanely popular. Mums are seen as more pushy because of the traditional homemaker divide, women are traditionally seen as the homemaker/ones bringing up the kids. It’s hard to describe this… its just vey different, if I did an aibu about my mother, people would be encouraging me to go non-contact! But it’s just different, the constant pushing is just kind of tough love.
In terms of marriage (while this is slowly changing) when you marry your obviously marrying your husband but its kind of so much more, your basically marrying into the family in quite an intense way, for example typically (although this is slowly changing) as a daughter in law, your going to your husbands family for major holidays (and your doing the grunt work). So its seen by parents acceptable to kind of push for their ideal partner!
Duo which is a dating app, has like 100s of questions asking even your parents profession, so it’s kind of just woven through dating not just parents being pushy.
Everyone takes their shoes off by the front door, leading to characters in haute couture shuffling around the indoor scenes in fluffy mules (even the men)
100% true, in Korea and for pretty much all Koreans that have moved abroad, I never wear shoes inside my own home. I'm pretty much as British as I can be, lived here the majority of life, went to school here, but that's one thing I can never get on board with 
take off your outside shoes! Don’t be traipsing in the outside dirt!! –omg Im turning into my mother-- Traditionally you would eat and sleep on the floor, and people still do, so it’s kind of from that, at my gran’s house, we eat off a low table and sit on the floor and she sleeps on the floor which is traditionally heated, called an ondol. you wouldn’t wear shoes in bed or on your kitchen seat so it comes from that, this culture is common throughout Asia, Japan also does this. People tend to have some spare slippers in their entrance way you can use. My mother carries around slippers in her handbag, as you do!
A certain naiveté in male:female relations, even for protagonists in their twenties, with little prior experience, touching or nudity. Is sex before marriage still quite uncommon in Korean society? The romances seem rather chaste to western eyes.
So this is kind of a difficult one to explain, the best way to describe it is kdramas to Korea are like Pinterest to the UK, for lots of them, they're supposed to be "amazing" like the ideal, the handsome guy, the cute innocent woman to be protected, the amazing food, the beautiful apartments, the couples acting cutesy rather than kind of raunchy. So that's kind of what people what perceive as the ideal relationship/goal/way of acting, but realistically people vary everywhere and while it might be seen as the best, young people sleep with others before they get married etc, they just won't be telling their parents about it! Korea is more conservative than the UK in terms of dating, lots of people live with their parents for a lot longer then we do, which prevents kind of what we would class as the normal dating experience and it's not seen as the done thing really to live with your boyfriend before marrying by the older generation, but on the whole people vary so it's not an everyone does X situation. When I brought this up with my cousin, she commented on its kind of messed up that there is this kind of thing of push on women to be innocent, when men are doing fucked up things like spy cameras in toilet doors, which is a big problem, english link below.
www.thesun.co.uk/news/6503756/south-korea-spy-hole-craze-womens-toilets/ < uk link to that
With so much product placement for Subway etc is a western diet creeping in and are people getting fatter? Everyone is so enviably slim
So you get fat people, but its less then in the West, in my grandmas village, no one is fat, you walk everywhere, you eat traditional foods, you home cook everything (and grow most of the food!). The fatter people you will find in the cities, fast food is a huge part of that, sizes are generally a lot smaller then in the uk, but in places like Busan and Seoul, you can order fastfood to your door 24/7, also desk jobs
There is a pretty unhealthy culture of fat shaming, which kind of leads into my next point. One thing I think is a serious problem, is on the other side of the scales, is the unhealthy diets (mostly women) follow to lose weight, mostly fueled by actresses and pop stars doing them, I’ve lost track of the number of weird diets my cousin (who is the size of a stick) and her friends have done, memorable ones were eating only sweet potatoes and another where it was some weird combo of I think only carrots and eggs, all day. Bizarre and such an unhealthy relationship with food.
Despite the boom in fast food and the unhealthy diets targeted at women, I think by and large, Korea has a healthier approach to food then perhaps we have here, at least in more rural places then the cities.
Some good examples of this are a program about food in the army: which is quite different from food I’ve seen about the British army I’ve seen on tv.
And some examples of school lunches on youtube:
Links about the obesity
Kids weaker and bigger then their parents koreabizwire.com/young-south-koreans-bigger-weaker-than-their-parents/111241
If you have Netflix I think it's on, Kim's convenience is a pretty much accurate description of Korean parents when they've moved abroad! Scarily so!
I will answer other questions later! Have to head out now, as I said though, this is just my take on it, from my family perspective!