"I'm sorry. Thank you."
미안하다 or 미안합니다 should be accepted. nleconte said the point. It is true that 고맙습니다 implies the more formal way of saying but the difference is slight.
It should be, but in that case, following "Thank you" should be "고맙다"(or "고마워"), not "고맙습니다".
송. As far as I know, every syllable contains must have at least one vowel in Korean.
You can also see that in some typical Konglish words.
As Korean does not have the sta combination, one has to put the s by itself. However, a vowel is required for every syllable, so very often the neutral ㅡ vowel is used, leading to 스.
It should be "song (ㅅ + ㅗ + ㅇ)".
Korean is written as blocks consisting of several characters and each block represents one syllable.
What you are referring to is the second character of the block and for any block, it should always be a vowel. Additionally, the first and third characters of a block should always be consonants as you can see with ㅅ and ㅇ.
This concept is better explained with visuals. Take a look here: https://www.howtostudykorean.com/unit0/unit0lesson1/
I think its just that one is pure korean and one is sino-korean. People use either all the time.
Is the rule here to pick the most formal one every time? Because it's super frustrating that every question has three synonymous phrases in the answer choices, and later questions define all the phrases as the same