A verb stem plus 기(ghee) plus 때문에 (ddemooney) is what you do with a verb before “because.” Here is an example: 내가 보기 때무에 행복 해요. (nega boghee ddemooney hengbok heyo) = I am happy because I am looking. Sometimes that 기 on the end of a verb can mean the infinitive form, and sometimes it can be the “-ing” form, either the actual verb inside a sentence or a gerund. Another good example would be: 자기때문에 한드폰을 들지 안았어요. (Jaghee ddemooney handu pon ool dulji an asseoyo) =I didn’t hear the phone because I was sleeping. 때문에 (ddemooney) means “because,” and the word order is different from English. In English, we give the results first, and the reason second. In Korean, they give the reason first and the results second.
You can use the 기 (ghee) form of the verb in other ways too. 자기전에 ( jaghee john ey) means “before sleeping.” They use this 기 (ghee) form that could be either a gerund or an infinitive. In English, we use the gerund form. 노래 하기는 재미 있어요. (nore haghee nun jemee eessoyo) = It is fun to sing. This uses the infinitive “to sing” in English and the 기 (ghee) form of the verb in Korean: 노래 하기 (nore haghee). 노리 하기 can be either the infinitive form or the gerund form. You could also say for this in English “Singing is fun” and use the gerund form making “singing” a noun whereas “to sing” in English is part of the verb.
When you use the 아/어/여/서요, it is a less formal way of speaking that is still polite that you can use with everyone, and it is the way the verb ends at the end of a sentence. If you are an adult, this is a good form to learn to use with most people. The only people you shouldn’t use it with are grandparents or a group of people you don’t know. It is not the lowest level of speech, neither is it the most formal way of speaking, but a good medium, friendly ground.
If you know the 습니다 (subneedah) ending for the verb, it is the ending for the more formal way of speaking. Here are some examples of the difference in the levels:
봐요 (bo-ah yo) = see or sees (This is a form you can use with most people.)
보슴니다 (bo subneeda) = see or sees (This is used if you are talking to a large group of strangers, to grandparents, or to your boss)
먹어요 (mogoyo) = eat or eats (This is the form you can use with most people.)
먹숩니다 (moksubneeda) = eat or eats (This is the form you can use with large groups of strangers, grandparents, or your boss.)
These two (요 and 습니다) are verb ending used at the end of a sentence. The difference is just who you are talking to and what your relationship to them is.