When plot cards are revealed does the moving of the previous plot card, and hence any affects thereof, including prize, occur in step 4b.- i.e. after all the When Revealed

4b: Passive effects to anything that happened in 1a-4a.iii each goes through "initiate-save/cancel-resolve" (e.g.: this is where you draw the card for Golden Tooth Mines

For new characters such as HDE and there is a double Valaar, would these guys get affected after the first one if all my Lannister characters were killed ~ or do them being in moribund still make HDE immune

If you control a [Lannister] character, House Dayne Escort gains "immune to plot effects."

No moribund characters leave play until all plots are resolved, so House Dayne Escort retains its plot immunity through a double Valar.

1. Yes, Prized on plots is a passive effect initiated by the plot being sent to the used pile. Since that occurs at the same time the new plot is revealed, any "when revealed" effect on the new plot (and any other plots revealed with it in the plot phase) will resolve before Prized.

2. As Grim says, characters killed by a first plot are still going to be moribund and physically on the table through any other plot effect, plus passives and responses to revealing plots. So the House Dayne Escort will retain its plot immunity until the entire action window for revealing plots closes.