What happened to Prime Elizabeth after Burial at Sea?

At the end of the Burial at Sea DLC, we see that:

Elizabeth dies protecting Sally and sets the events of 1st Bioshock

So does that mean based on the ending of both the Burial at Sea DLCs.

Are both Prime Comstock/Booker and Prime Elizabeth dead?

I'll make this as simple as I can.

There is no Prime Comstock and Prime Elizabeth, as there are multiple Elizabeths and Bookers and calling one of them Prime is a bad idea.

Essentially the Elizabeth from Infinite and BaS Ep1 is dead at the start of Episode 2. The Elizabeth that we are playing as sees her other dead self.

The Elizabeth that that we are playing as is from a different timeline where she feels regret for leaving Sally in the vent to die. She came to this timeline to rescue our Sally from the same fate. She looked through all of the tears and found the one instance where she had killed Comstock and died herself.

Yes, all Bookers are dead because the one that went down to Rapture in order to find his daughter is dead. All of the rest were drowned at the end of Infinite.

I'm also adding the definitive video that I've found that explains the entire story. It's a GREAT watch: Here you go