If a teacher says "long time no see" to a student who has been absent without excuse from the last six classroom sessions, it would be most likely be interpreted as sarcastic, and would express displeasure at the student's sudden appearance with no explanation for his absences - unless the teacher really likes the student, then it would be interpreted as a friendly and enthusiastic welcoming back
"I'll catch you later" is an abrupt and rude way of departing. If a person says this, it would imply that you don't mean much to him. This is not in the least true where I live. I live in Canada. May I ask where you live?