With skill his story will unfold
Re: Zombie Serum: Single-Use and Not-On-Frank [OPINION ONLY?]
Nothing on the "Zombie Serum" card or glossary tells you to discard it after making a zombie. But Scenario 4 has a special rule that suggests it normally would be discarded. I prefer to discard it - hope you and your opponents can agree amicably.
Also Frank... I assume he can't be raised when killed, but I wouldn't want to rely on the rules to convince you. Because in every other way (Jeff; Zombie Control Device) I think he is treated as not-a-zombie.
The Zombie Serum card has a 1-shot ammo icon at the top-left, which makes it single use. See p 23 "Special Items with Limited Number of Uses".
When Franck is dead, he is a cadaver, good for making zombies out of. He doesn't come back as Franck, though. See p43 "Zombie Serum".