Those are a lot of questions but let me see if I can answer being a frequent Southwest traveler with a child. 1. You are allowed 2 bags per ticketed passenger free. 2. You can gate check the stroller and car seat with the base attached. I've typically seen these (car seats) come out at baggage claim inside a big plastic bag. Probably to prevent the base separating from the seat and to keep them clean. I'm not sure whether the airlines provided that bag or if the passengers brought it with them. Think transparent large trash bag for a visual. I have see double wide strollers gate checked. 3. The baggage policies apply to all passengers regardless of whether you paid full fare for your ticket or are flying on a companion pass. 4. Boarding is the same for all types of tickets. The ONLY exception would be if you are flying stand-by. If that is the case (as you indicate it could be via your "if there are open seats" remark) then it is possible that the gate agent may not know if you'll be able to fly until the last minute (typically 10 minutes before a flight as that is when people that have not checked in and are not near the gate area are in danger of losing their seats) so if that is the case, you would be possibly the last person to board the plane. If, however, they give you a seat prior to boarding then yes you could board during family boarding which is after group A and before group B. Hope this helped!
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