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.
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Yes and yes. "to" is more formally proper, but "and" would be usual in everyday speech.
teacherJapanI’ll come and see you
That's correct. Omitting and in such examples is a feature of American English.