Different publications have different ( answers) to all of your questions. Each one has information listed ( or a link to visit) for submission requirements/ guidelines, etc. so, start with magazines you are interested in and see what their requirements and policies are.
some ( hold) the rights to the pattern, some allow you to keep the rights. I ( think) most offer some sort of compensation. Sometimes it is only free subscriptions, the publicity, and possible sales of your ( kits).... Sore pay you for the pattern, then they choose how / if it will be featured ... Some require the actual finished quilt be sent in for their own photo shoot. I've never heard of you needing ( proof of show quilts or anything like that as a requirement)
pthe biggest rule is make sure it is Original, really yours. Well written and tested. Check that there are no typos, grammar errors, the math is right, the cutting , diagrams, illustrations, are all easy to understand and accurate.
Some magazines have you submit your ( proposed ) project & picture of tested quilt then they have people who actually write the pattern.... Like I said in the beginning....there are lots of ways & lots of different publications. Start with your favorites that carry patterns are compliment your style, type of quilt you plan to submit.
I know TQPM ( The Quilt Pattern Magazine) is looking for new submissions right now.