Looks like you're set for the food element.
So I'll add something about the drinks.
There are several domestic beers available here. None of which I like, still haven't got used to them after 8 years. But certainly try them all, but I find they leave a weird after taste. Makju, pronounced Mekchoo. Eating chicken and drinking beer, ChiMek.
Soju, is of course extremely popular, just be careful, it'll knock yer socks off. This can be bought in any grocery stores and bars and restaurants. The quality can vary, from a couple of bucks for a bottle to 20 bucks a bottle (KW2000 ~ KW20,000). The cheap stuff is made predominantly from chemicals, the more expensive stuff is distilled from rice and is usually stronger and a much higher quality.
A favourite thing to do is to mix a shot of Soju with a glass of beer, thereby calling it "So-Mek".
Bokbunja, is very drinkable. It's made from raspberries and other berries, quite sweet but delicious.
Makgeoli, is a fermented rice wine. Very refreshing in the summer time. You'll need to gently up-turn the bottle to allow for the sedimentation, don't shake it, it'll go everywhere, as its very lively.
Try everything at least once.
As an aside regarding food, dog restaurants do exist. We used to run a hiking club where I am located and we would often times end up walking past the occasional dog farm.
I have never eaten dog, nor do I have any notion of eating dog, but each to their own.
BTW, I've only been to Seoul a couple times and have no idea about where or what to do. I'm located way down south on an island just off the mainland, called Geoje.
Enjoy!