Two questions that I believe I know the answer too but would like some outside input

1) during our first agenda phase everyone (except me) announced they were playing a rider. We went in turn order to resolve the cards. The last player, played a veto action card. Since the last card played vetoed the agenda, do all of the rider action cards jave no effect and just get discarded or do the stay until the next agenda card?

2) during the agenda phase I had a player try to play two rider action cards. The cards were of a different name and effect. Can both be played or does the text about not voting make the next card invalid? I believe this may also fall under the "action cards can't be played that effect the same tjings," I'm paraphrasing but I hope you get where I'm headed.

Thank you