Hello To answer your first question, '전화번호 좀 가르쳐 주세요,' is used to ask someone for their number. This could mean their land line or cell phone number. '좀' is an abbreviation of 조금(which means little) just like what torch wielding guy said in the comment. It is used to make a request sound less imposing, and is used all the time in day to day conversations. Take for instance, '물 좀 갖다주라.' This means 'could you pass me the water? OR pass me the water will you?' Without '좀' you could say, '물 갖다줘,' and this would mean 'pass me the water,' and would sound more like an order than a request.'

좀 (abbreviation of 조금) means "a little/some", but is often used to soften a request.

thank you!:))

전화번호 좀 가르쳐 주세요 ~ Tell me your phone number, please /// 좀 ~ please /// 가르치다 ~ teach (^ㅅ^)