Andromeda is not (and will not) story additions, so Access will post the full finished version of the game. Dead Space 3 is already a backward compatible game. For the past couple of years, EA have been adding more and more games to the Vault, strengthening the value of EA Access as a whole. No exact dates were given.
Andromeda has registered poor sales at its beginnings due to the fact that it was maligned upon its release. Many of these issues have been fixed to varying degrees, but those amendments came well after weak sales which have reportedly resulted in changes to developer Bioware and the franchise's future. Issues regarding the game's facial animations and overall performance made for quite a lot of meme-worthy content when the game was first released earlier this year. The Battlefront 2 blurb isn't specific about whether the number of trial hours are limited, while Payback says it'll be restricted to 10 hours ahead of launch.
EA did not disclose when exactly will these games and trials be available for subscribers, only that they will land before December this year. With the console launch of The Sims 4 slated for next month, EA Access subscribers on the Xbox One will also receive a Play First Trial for the simulation game before its launch.
Lastly, Dead Space 3 will be entering the Vault, meaning that the entire Dead Space series is now available through EA and Origin Access in some capacity. To benefit from these options, users need to have a subscription.