In a deposition, do only lawyer asking the questions talk? or can his client, plaintiff, also chime in?

Your attorney can object to any questions from or made via the other party through counsel. It's bad form for an attorney to allow the client to "run" the deposition. It says a lot about the attorney's lack of client control and/or lack of preparation for the deposition. There may be no hard and fast rule in your jurisdiction to prevent this. Nevertheless an objection can be made and the matter can be brought to the attention of the court for direction or sanctions or anticipatory orders for further depositions.