Great job!
Of course there are at least a dozen equally valid ways to say something; therefore, without getting into choice of words, expressions, or phrases, let's concentrate mainly on the grammar.
그래서 형의 일하시느라 준혁누나의 결혼식에 참석하지 못하셨죠? 집에 아무도 없죠? 진짜 외롭겠다!
저는 전공을 늦게 바꿨으니까 12월에 졸업할건데요!
형
의 일
때문에
그래서 형
이 일
하시느라
형의 (Brother's -possessive) 형
의 일
때문에 "because of 'your' work"
형이 ("Brother" -may perform an 하다 action) 형
이 일
하시느라 "'you' busy with work"
These sentences look grammatically correct to me
집에 아무도 없죠? 진짜 외롭겠다! however, some points to watch are:
tense
The previous sentence is set in the past, but the two sentences that follow are in the present tense; normally we would imagine a conversation
after the event and all sentences would be in the past tense, UNLESS you are NOW talking to "형" on the phone, say, JUST AFTER the wedding. So to be sure your intended meaning is clear pay close attention to tense.
respect form
If you start out with a certain level of respect 일하
시느라 - 못하
셨죠 be sure to maintain it throughout the entire range of conversation 진짜 외로우
시겠다! It may be acceptable to use the informal ending '다' because the exclamation is somewhat retrospective, but you should still use honorific 시 to describe any action or condition of that person being respected. And in my opinion it would still be a good idea to use polite form '요,' in keeping with the other statements. 진짜 외로우시겠군요!
The grammar here also looks fine to me
저는 전공을 늦게 바꿨으니까 12월에 졸업할건데요
! but the statement wording does not appear exclamative so drop the "!" You might reword it something like this 저는 전공을 늦게 바꿨으니까 12월까지 졸업 못 한단말이에요! to give it an exclamative feel. "Because I changed my major late I won't graduate until December!"
