Networking: issues with replication

1.Seams like begin play has wrong implementation/name and instead of “call when everything done” is “call when construction script of this exact object is done” which means it cannot rely on any other objects, even basic one: you cant rely on player controller existence on level begin play. Also there are delay between PIE sessions created and clients connected to them, so there are another issue, you might call the object which is exist only on server and not yet replicated.
2. I dont understand what you asking, so lets rebuild the question
What you want to happen (exact effect what you want to achive)
When you want it to happen (what cause this effect)
Where you want it to happen (what object you want to have this functionality)
go on.