Hi OP:
When you received your DS3025 was it marked complete? If it is then no further action needs to be taken for AOS purposes. Hep B is similar to MMR in that it is a multi-dose series and a waiver is given because insufficient time to complete it. As long as you have one shot, you're good as Mallory says there- though if you'd like to finish the series for your own health reasons do so. Attach a copy of the form when filing AOS, as long as you do so sooner rather than later. K1s are not required to redo their medical in the US if their form is complete. If you do not have the required vaccines, are not marked complete, are missing some, or need to obtain them after having the medical or after you are in the US - you will need proof of each one, and will need to see a US civil surgeon to transcribe and recertify. As you can see here in the AOS guide:
As for anything else in this thread, AOS is very important to complete as soon as possible after being married. To delay puts the immigrant out of status and subject to deportation. There are certainly reasons some people delay, and you will find plenty of examples as to the consequences. Make sure to file in a reasonable timeframe, and as you can see above you want to do so before your medical results expire. You do not need to carry around your marriage certificate, as that confers absolutely no legal status. Marriage is a state's rights issue, and not a federal domain - where immigration resides and is mostly all that matters. Once you file AOS your NOA1 is your proof, followed by an EAD (if hopefully also filed for).