Not sure on the Gatwick question but I would guess No
Departing from Dublin on an EI flight I don't think you will get fast track regardless of BA status or whether your ticket is BA stock or EI stock .. in fact in my experience you probably won't be able to check in online, assign seats or anything if it's a BA ticket as BA and EI IT systems don't play nicely together .. go for a BA operated flight if possible to make it simpler.