Main tecnology in Andromeda?

The Mass Effect technology will be extremely present, might even be the biggest one. I wouldn't even be surprised if the have a couple of small relays in there, or the plans to build them.

From the E3 trailer, the Kett used laser guns, like Star Wars.

I think it's fairly clear that the Remnant tech will fulfill this role...which I suspect may be I'm sure it will have a number of other helpful applications as well.

That's a sound theory.

The E3'15 trailer hinted at rapid buildings that just grow from the ground, it might be connected to that. 

Going by how there seems to be a black hole in the middle of the Heleus cluster, their technology is probably gravity (waves) based (like that gravity well in the trailer) instead of eezo based (even if eezo should be present). The Milkies are going to bring their mass effect tech there and clash with it. Mass effect is basically the anti-gravity.



Also, the threat of time travel and other weird temporal shenanigan is probably looming over us.

Biotechnology & organic-based tech? they would be interesting and incredibly terrifying to watch. Perhaps some Lovecraftian influence?

I don't necessarily agree about FTL travel. The speed of light is a hard barrier. I'd not at all be disappointed to learn that the mass effect is the only way to bypass it. Maybe hyper-advanced species, well beyond our imaginations, have achieved other means; but the kett seem to be more or less on our level. If they do have a different means, though, I'm equally okay with that.

The good news is that "their tech" will be a bit different than "our tech". Mac confirmed via tweet some time back that "the species of the Andromeda Initiative" would be using mass effect technology. His specificity seemed to imply that the tech of Andromeda would be, at least in the majority, developed from different starting point.

I've been saying for months how I'd like to see the impact of introducing mass effect technology to Andromeda explored, if we truly do so. (I have my doubts as to whether we truly do.) I'm pretty certain that this will not be a theme, but it could've been interesting to explore.

Some of the kett weapons definitely have that sort of look to them. Who knows what the basis of their tech is, though? Even though Collector weaponry looked organic and "different", it was still built upon the mass effect.

It kinda goes back to original trilogy. Reapers groomed MW in certain way, so they would be dependent on Eezo, if it was the only way then why bother with shaping MW progress into certain tech tree? 
Besides our science already has two theoretic ways to bypass speed of light.

I think we do. Biotics abilities are the result of eezo exposure in very young age/before birth, so eezo starts to gather in neurous system and eventually it adapts (unless host dies) to use eezo with neural electricity.
Thessia has eezo rich enviroment, so all asari there are exposed to it by default. As for their colonies - well, pregnant asari there probably need to eat some eezo cupcakes if they need their children to be good at biotics.

None of human biotics are natural and are result of "accidental" leaks of eezo in highly populated areas, so they have no more reasons to die out than in MW galaxy. We might encounter many non-biotic asari in the future though, if their parents decide not to undergo proper treatment.

Theories have a way of turning out to be BS. I'd be fine if eezo were the universe's sole trick for bypassing the speed-of-light barrier. I'd also be fine if the remnant used some type if I standouts wormhole tech, or any other space magic. All of it is equally ridiculous, and equally acceptable, if cloaked in the right in-game tech-babble.

Since eezo is a natural part of the universe, I'm sure we will see biotic species in Andromeda. I'd not be surprised if the kett have biotics among them.

I'm sure diminishing biotic potential falls well outside the scope of the games. The asari could very well have elevated element zero levels high on their list of preferred traits for colony worlds in Andromeda. They could continue supplementing their food and drink, I imagine, indefinitely*. (Setting up eezo mining and refining will be an immediate priority in Andromeda, so they'd have a supply.) They developed biotics "naturally", through no conscious effort of their own. They should be able to maintain the status quo via dietary supplementation, indefinitely.

*The wiki page for Thessia mentions that restaurants on Thessia serve a small side of eezo with food and drink. Seems strange, but it would allow the asari to maintain their species' adaptation wherever they went in the galaxy/universe. There's a visitor menu that doesn't cause horrific death via toxic sides. This bit of "trivia" has no cited source, so I am skeptical as to its origin.