The latter one is gramatically correct, but neither makes sense since nobody drinks coffee because he/she just had a haircut. "머리 자르고 커피 마셔요" would be what you mean. 잘라서: because 잘라도: even though 자르고: after

Here is the answer to your comment: As you mentioned, ~서 can provide background information that are related to the location and position: 식탁에 앉아서 대화를 나누다: to talk to each other sitting at the table. 침대에 누워서 음악을 듣다: to listen to the music lying in the bed. As you can see in the examples, it can be translated to gerund in English. 학교에 가서 숙제를 하다: to go to school and do the homework there 집에 와서 잠을 자다: to come home and sleep 시장에 가서 점심을 먹다: to go to the market and have lunch there In these examples however, it's related to locations. As you can see, ~서 conjunction can provide information of importance about the status/location. If you want to express the importance of having coffee AFTER the haircut, you should say: "머리를 자르고 나서 커피를 마셔요"

Thank you a lot!

Yes. The pattern for 고 is simply that - 고. Drop 다 and add 고. For 서, the pattern is 아/어/여서. Drop 다 and add the appropriate variation, based on the same way you would conjugate in 반말 or the 요 form. Ex. 먹다: 먹고, 먹어서. 마시다: 마시고, 마셔서. 하다: 하고, 해서.

고 could translate to "and" or "and then", but 고 나서 definitively illustrates the latter (and then, blah blah AND AFTERWARDS blah blah)