You can order the day of your Haunt visit, if you're a procrastinator like me. As Gabe said, nothing is mailed. Instead, you have to process the pass at the park. When you order online, you'll get a PDF file with a voucher for each pass; print those out and take them to the season pass processing center (door on the left side of the ticket sales building) when you arrive at the park. They'll take your photos there and hand you a season pass card for each voucher.
Your one free visit will already be loaded onto that card. Your vouchers probably will not work for parking, so don't use the self-scan lanes and instead pay normally at the toll booth (I think it's $20), then go to the ticket windows after you process and show your pass and parking receipt. The sales associates there should be able to issue a refund.
I have no idea regarding your question about using the free parking again for Winterfest. My guess is that it might not work, but I could be wrong.
Again, as Gabe said, the lowest prices of the season are now. Beginning right after Haunt, they will start going up, and they will only continue to go up. Unlike some other parks, Kings Island does not typically put their passes on sale at any point of the year, so whatever price you see for a pass at a given point in time is the lowest price you'll ever see for that pass for that year.