Both are manageable in Korea, but neither is handled by asking casually. Written communication is the reliable route.
The densest concentration is around the Seoul Central Mosque in Itaewon, where certified and Muslim-friendly restaurants cluster within a few streets. The Korea Tourism Organization publishes a classification — certified, self-certified, Muslim-friendly and pork-free — and restaurants display it. Outside Seoul, Busan and Jeju have small clusters, and university areas often have halal options for international students.
Pork is the default meat in Korean cooking. Pork stock appears in stews, pork belly is the standard grill, and even seemingly neutral dishes may be seasoned with it. 'No pork' therefore needs to be stated explicitly rather than assumed from a dish being fish or vegetable based. Seafood restaurants and temple food are the two easiest categories.
Speak less, show more. A written card naming the allergen in Korean is far more reliable than a spoken request, because it can be carried to the kitchen. Sesame and sesame oil are extremely common and are the allergen most often missed; peanuts are less common in Korean cooking than in Southeast Asian.
Anchovy and beef stock in almost every soup. Shrimp paste in most kimchi. Sesame oil in nearly all seasoned vegetables. Soy in practically everything. Egg in the garnish of many rice dishes. If an allergy is severe, dishes cooked to order are safer than pre-prepared side dishes, where you cannot ask about each one.