Sometimes when there's two vowels next to each other in Korean (like when adding an ending to a word that also ends in a vowel), the two vowels contract so it's easier to say.
For example, instead if saying something like 행복하여요 (haengbokhayeoyo), which basically means "it is happy", the third and fourth syllables would contract to 행복해요 (haengbokhaeyo). It still means the same thing, it's just easier and smoother to say. There's quite a few different rules for conjugations of different character combinations (including some with consonants as well), but you don't really have to worry about most of them until later on. Just know that conjugating doesn't change the meaning, it just makes it easier to say. :)
Difference between "my" and "i am". Here are example sentences: 나는 개다 I am a dog. naneun gaeda. 내 강아지 My dog. nae gang-aji. (강아지 is another way to say "dog") "My" = "내", which is a contraction of "나의" - less formal "My" = "제", which is a contraction of "저의" - more formal. "I am" = "나는" naneun. And a more formal way to say “I am” = 저는 jeoneun.
So, this sounds like 저 헤 개 to me, which is unexpected from the spelling. Like 죄. That's not a complaint, I can just learn it that way. But it sounded different when attached to another word, I think. Does -의 always have an -ay kind of sound, or does it depend on context, with the word it goes on?