A - Object particle -를 / -을
This particle follows the object. "를" is used after syllables ending with a vowel, and "을" after syllables ending with a consonant.
B - Introduction to locative particle -에
The locative particle "-에" is tricky to use. This is why we will only study one of its many uses for now: -에 가다, which means "to go to..." a given place.
C - How to express "and", "with" in Korean -와 / -과
There is a way to express prepositions "and", "with" in Korean, using the proposition "-와/-과", which works as a particle. "와" is used after open syllables, and "과" after closed syllables. The adverb "같이", which means "together" can be added to clarify the meaning of the sentence.
D - Interrogative pronoun 무엇
The interrogative pronoun "무엇" means "what". It can also be contracted to become "뭐". In the case of "무엇 + 을", that is to say the interrogative pronoun followed by the object particle, it can be contracted to "뭘".
Translations of the texts
John: Hello. I am John.
Lee Hyeon-ae: Hello. I am Lee Hyeon-ae. Pleased to meet you.
John: Pleased to meet you.
Lee Hyeon-ae: John is (are you) a student?
John: Yes, (I am) a student of the College of Oriental Languages.
Lee Hyeon-ae : I am a student of Seoul National University.
John: Hello, Kim Tae-ho.
Kim Tae-ho: Hello, John. Where are you going?
John: (I) am going to the library. What are you doing?
Kim Tae-ho: I am studying too. Then I will go with you.