What's usage of 서 in the sentence 나가서 사드세요?
I guess this is a sentence with honorific to say"Please go out and buy XX"
But what's the usuage of 서 here?

Question

Answer

~서 can be used with a "sequence"

돌려서 빼 Turn and (then) pull.
나가서 사드세요. Please go out and then buy something to eat. ('사먹다' is to eat out, as opposed to eat at home).

~서 can be also used with "cause and effect"

나는 피곤해서 지금 잘래. I'm tired, so I'll sleep now.

Answer

"서"  in that case means action order, something like "then".

Answer

"and"? 
Perhaps to connect two clauses that are following each other in time? Well, at least in imperative sentence

집에서 편안하게 언어를 배울 수 있는 기회를 놓치지 마세요. 경험 많은 강사진을 살펴보고 지금 바로 첫 수업을 신청하세요!