1) I picked 'I don't care about size, the story is top priority', but I give respect to 'nice balance' and 'story oriented'. Basically, I just hope Bioware doesn't annoyingly and incorrectly focus on there being such biggg worldddssss that they screw up their game in the process. And I think they just nearly did that with DAI. But I can like larger 'zones' and a vehicle to drive isn't necessarily a bad thing and explorable areas that go beyond what was effectively often a shooting gallery in the trilogy.. I'm okay with that.
2) Geth, in some form. I left other answers for others to make, and went with my personal fav, since I wasn't allowed to give a 'top 3/5/etc'. While, say, Salarians have gotten 0 so far, I hope anyone from Bioware looking at this doesn't mistake this for dislike for them. We've simply not had enough of them in great ways yet. (ME1 Virmire team, ME2 Mordin, ME3 Sur'Kesh is all nice but still less important and interesting than the other 2 Council species). Same goes for the 'joke' species: elcor, hanar, volus.
EDIT: I did pick Destroy, but I have various ideas on how Geth could be reintroduced without it looking excessively contrived. I still think the Destroy choice was important and should be considered important by Bioware. But this doesn't necessarily mean 'no Geth' to me.
3) Play as my companions. I want to be able to switch between them in battle, at least. Not against War Table but only the final version of it in recent patches was remotely high quality. Seemed like a half feature. I don't care for an 'open world', I only want relatively larger areas compared to previously (or rather, ME1 sized areas but polished as much as ME2-ME3 had theirs). I'm not afraid of DAI impact on MEA as long as it has the lessons learned from DAI, not the mistakes.
4) I'd like to see the ME3 ending have an impact on MEA. Yes. I'd like the whole trilogy to matter to an extent. However, I give respect to those who want a 'fresh start'. I want context to change but I'm okay in this specific case for only context to change, not any more core gameplay (whereas ME2 had various sidemissions and ME3 had war assets and such). I really would like to see familiar faces, and see the story relate to ME3, but I also want such faces and relations to be, at least in most of the larger forms they could happen, be an optional layer of development for the devs and not exactly core (like for example, having TIM in ME3 because he was set up in ME2; of course that had to happen, but I'm saying none of this should happen for MEA in relation to ME3). I'm not afraid of a connection, I only also understand that MEA will be a fully new generation for the series and Bioware can and should deal with something new before the old (and then involve the old if they have the time/resources/will/story for it). I'm not going to cry if for example they don't even mention Legion, but I would be very happy if something of Legion did happen in even a main mission. Just do some things, at least.
In some of my vague theories about the series, it involves Andromeda being more of an intentional departure from the trilogy BUT THEN we actually go back in full force to the Milky Way. If that's the case, then yeah, go on that departure, have us learn many things and advance the series in ways the trilogy was restrained about... but then freak out (in a good way) all the fans by bringing that experience (in game development and plot) back 'home' in a 'ME5' in 2018-2020
. Basically, I'm fine with a big 'field trip' to 'explore', but I'm never going to let go of what was started with the Trilogy and IMO deserves more than just the 'maybe possible slight callout'. I'm not a 'total fresh start and never look back'er - I just respect the sentiment and I'm okay with that being MOST of MEA. Just not all.
I don't understand what is meant from 'updated quest system'. Looks like it doesn't belong here.