1) Yes, you must pay the Sevis fee again for a new F1 since it has been more than 12 months since your last Sevis payment(student status).
2) Resume is not required but good to take it with you if you have one.
3) Yes, it is ok to say that you worked on OPT and H1B. Actually, it's better to disclose all info that pertains to your legal work that you did while in the US. If your income specifically came from working in the US, make sure to to mention it. They can see all your visa status and work authorizations anyway so no need for secrecy if everything was done legally.