1. CBSA usually cross out the PRTD (single diagonal line) as its a 1 time entry document.
2. She will not get anything else - in fact CBSA may not stamp her passport. If this happens she should politely request for a physical entry stamp.
3. She should use the other documents listed as acceptable for BC care application.
4. On the presumption she is a South Korean national is there a reason she applied for a PRTD? As a non visitor visa exempt national she should have just traveled to Canada and dealt with CBSA at the border. PRTDs (despite CIC's notice to the contrary) are practically only really necessary for non visitor visa exempt nationals so they can board a flight back to Canada with the airline safe in the knowledge they won't get bounced and land the airline with removal costs. You save 50 bucks plus associated costs this way and have the expired PR Card to hand for renewal or any other (limited) process that will accept an expired PR Card.