Hi I'm South African (White) and can answer some Q's for you:

Games depend from place to place and culture to culture since SA has a diverse culture from White shout Africans to (Not meant to offend) black South Africans (Zulu, Xhosa, Sotho, etc.) But some games I played growing op on were hop scotch, hide and seek, 'touchers', and also we would hoela-hoop and jump rope a lot, other "outside" activities included swimming in the river (You can't do that now but 14 years ago still could - water in the rivers are know very polluted compared to then) handstands races, climbing trees and making mud balls. traditional toys that are still popular and fun to play with are hand crafted wire toys, cares made from wires that with a long rod you push and its wheels would turn, we would have races to see who's car was "faster" but really it was who ever ran faster ~LOL~
We also played frog jumps (where you hunch over and someone jumps over you then they hunch and you jump over them... And Ring-a-ring-a-rosie... oh and we as children loved to "bake" mud cakes and trick each other into eating it, thinking it's real cake or make "gross" drinks, again tricking whoever into drinking it thinking it's 'flat' soda or something ~LOL~

Traditional SA type snacks and food depend from province to province for Example most of SA people eat "pap" well that is except for Cape provinces they staple food would rather be bread, there are very few people there that eat pap.
Pap can be eaten either as breakfast with sugar and milk, or as a side dish or part of the main dish, depends on how you make it, we love to "braai" (BBQ) and with Braai we would eat pap. We have Biltong, chilli-bites, and droewors, these are beef meats (cuts) that are dries using spices (In America a similar snack/treat might be beef jerky... except it a lot more tough and salty than biltong, chili-bite, droewors, etc. that we make in SA) PS chilli-bites aren't necessarily spicy, but it can be depends on who made it.
We have "bunny-chow" this is especially common in Cape Provinces - it is basically a loaf of bread that is hollowed out and filled with curry. It is delish!!!
We have our own Chutney - Misses Balls not to be confused with how Indian or Thai chutney tastes! We use it as a sauce with most meat dishes, if want, like ketchup, some even use it in their own Chakka-lacka recipes or pasta sauce recipes!
Then we have "Ouma Rusks" a fave to eat with coffee or tea for breakfast!
We also love our pastas, pizzas and burgers!

I'm not sure what you really mean by skin ship encourage?
And if I go with what I think you mean by it... I might end up righting a whole essay on racial matter in SA...

As for holidays I don't celebrate most of them since, most holidays are base on pagan believes even though "Cristian holidays" but we do have "Christmas" but it's not like every one goes full out to celebrate it, heck very few of my own friends rarely even put up a Christmas tree, though presents does seem to be handed around. Halloween... again nothing major happens around that holiday as what I imagine would be the case in America for example...? Shops would "advertise" it but there's no trick-or-treating or Halloween parties of the sorts, some restaurants would be decorated sometimes... but not drastically.
Easter again isn't celebrated with egg hunts or the likes as most South African's celebrate it as the Passover as in the Bible, so as with me and my friends and family we go to church gatherings/camps where we have pastors preaching and out reach programs.
New years... also not major.
Other Holiday events are Mother's day (Though don't always get off) it's important and everyone treats their mothers (Husbands their wives) as well valentines day is a bit more celebrated than Christmas as schools would have valentine balls.
We even have a special day call Braai Dag ~LOL~ 28 Spet.
Then Youth Day - with is more like a memorial regarding the Sharpsville strike where the youth protested for the chance to be educated in any language(s) - their mother language. - 16 June
"gelofde dag" which is on 16 December (if remember correctly) it the only day the sun shines through a hole at a monument which was built so exact, it's the Voortrekker monument - the monument was build on the promise the "boere" had made when they were at war with the Zulu's, the promise was to God, as they were being overwhelmed and caught in a difficult situation, they vowed that should they make it through they will devote that day to god, and hence they survived and went to built the monument. Since 2012 though, the government has declared it a normal day as it is a "racist" holiday, a reminder of "apartheid" though in actuality was before apartheid. But many a people still take the day off to go to church as the promise to God to devote the day to Him because He lead them to safety - that 'battle' is called (in Afrikaans) "die Oorlog by Bloed Rivier"

Stereotypes... mmm... I can't think of anything...

In South Africa there are various Cultures and just my explanation won't suffice, since there's Zulu traditions as well, or Xhosa, or Sotho, Venda Indian and Chinese even in SA.

In the "Boere" community, we have our own folk dances and folk songs as well, we like to "soekie dans" - that's a type of dance with a partner.
We have what we call "boere sport" which are games we play, like trying to eat an apple off a string without using your hands, or an apple in a bowl of water again without using hands, or getting jelly tots out of a plate of flour, or seeing who can eat the most "marie biscuits" without drinking anything (that biscuit dries up your mouth so much, you'll start to choke on it!) There's running with an egg on a spoon held in your mouth, balancing on a barrel while running on it (a race) three legged race, water balloon catching, every time you throw it and it's caught each person takes a step further away, the one that causes it to burst loses - there's so many different games, some include driving your car blind folded through a obstacle while someone you trust navigates you through it...
These games usually concludes with a bon fire and stick breads - bread dough that is put on a stick over the fire and when "baked" you break it off and eat it with cheese, and or jam or syrup.
We also have natural remedies for illnesses called "boere raad". These remedies are from - for coughs to asthma, 'cures' for cancer, to easy fixes for sun burn... And to be honest in most cases these remedies work like charms!

I got to commend you for reaching out and trying to be so inclusive and willing to expand your understanding of different culture. While I am not part of the above ethnic group, if you ever need Indian perspective feel free to message!

South Korean
I'm not South Korean, but a fantastic place to learn (in a TV way) about their culture...and you will see different unique social behaviors. Don't know how fast you need the info, but watch some KDrama, which will amaze you. Dramafever is the best place to start.

You'll learn a few of their delicious food, like Kimichi. And how sometimes family members care for one another while eating. Like Mom wrapping a lettuce or leafy veggie around some beef and allowing their son or partner to take a bite or gulf the whole thing down from Mom's hand.

Some families live without chairs in their homes. And theirs a boiler that heats the floors. These have good conflict...rich/poor...and family member (oh, food too)!

Some great shows to get you in the mindset are:
Pinocchio (it's got a big fantasy in it, but I loved it)
I Miss You Really Good!
Baker King Kim Tak Goo Great too!

Hope this is useful.

South Korea:

BEEF IS REALLY EXPENSIVE THERE. For some reason, eating scenes in Kdrama tend to show a lot of the beef lettuce wraps, but this is actually not commonly eaten, due to the exorbitant price of decent beef. Inexpensive ground beef products are VERY likely to contain pork, even when labeled 100% beef.

That said, Kdrama is still a good starting point. Just don't make it your only source.

Games kids play:

rubber string dance - two girls hold up a rubber string, and other girls dance around the string following a preset choreography. The string is held up higher and higher with each repetition of the song, and if you fail to cross your leg over the string when you're supposed to, you lose. This game supposedly originated from Japan and got imported during the Japanese occupation.

Gonggi (공기) - You have five pieces of gonggi toys; they're a bit bigger than M&Ms. You perform various tricks with those toys using your hand(s). The most common variation is 12345.

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Tags, red light-green light (called Rose of Sharon Has Bloomed over there), etc. all exist there. In the past decade or so, though, smartphone has taken over physical games. Kids are too glued to their phones to go out and play.

Couples hugging or kissing in public is frowned upon, though you do see it occasionally. This is a culture where even married couples avoid kissing in front of anyone, including (or perhaps especially) their own family. This isn't 100% about being prude... It's also about their emphasis on sharing and their concept of public. You don't share your romantic partner with others, not in a "here, everyone can take turn kissing my partner" way, so it's best to keep it private.

Same sex friends can walk around holding hands/ arms wrapped around each other's shoulders without being seen as a couple.

It's possible that none of this is relevant, though, if your Korean character has been living in another culture for a long time. From what I've seen, here in the US, 1.5th generation Korean immigrants who left Korea at an early age (like 10 and under?) tend to be entirely American, culturally speaking. Those who grew up in Koreatowns are exceptions for obvious reasons.