I’ll come and see you with the friend you met the other day.

Is this correct? Also, it it okay to use ‘to’ for the underlined part?


Yes and yes. "to" is more formally proper, but "and" would be usual in everyday speech.

Students: We have free audio pronunciation exercises.
teacherJapanI’ll come and see you

That's correct. Omitting and in such examples is a feature of American English.