There is no function called Init that comes with the FirstPersonCharacter by default. I assume you are calling this from EventBeginPlay. Try using a custom event node set to run on server that runs init instead. Then, call this custom event from EventBeginPlay.
You will probably have an issue with your pickup, as it is setting a replicated value without being run only on the server. This could yield bad results later on (server overwriting the value).
As for the projectile, it is not set to replicate at all by default. You will need to set it to replicate, and replicate movement in order to see it across clients.
Here are screenshots from my small bit of testing.
FirstPersonCharacter Blueprint:
Widget Variable Settings:
Projectile Replication:
Game Windows:
