It can mean the same thing as "catch a cold," but catch a cold means to get sick. "To catch a chill" can also mean to get cold, or to have a full-bodied tingling sensation associated with fever or sickness. EX: I usually catch a chill at the beach so I always bring a sweater. EX: I caught a chill a few moments before I vomited.

Yes it means the same thing :)

Yes, it could mean to catch a cold but it could also be slang for calm down but 'chill pill' might be used more so if it was slang

Yes it does.