DO official bioware lore experts exists?

Not to my knowledge. The mass effect wiki is fan-made. I think the closest thing to lore are the codexes, but even they aren't necessarily consistent from game to game.

Chris L'Etoile and clearly Drew K from reading Revelation and his other novels... but they left.

Which is sad. Lore should not be viewed as a chain to hold you back, but a guide to find creative ways to push a story forward.

also note that while L'Etoile was emplyed before the BioWare company culture shifted towards the more bureaucratic EA culture his successor in 3 Chris Hepler would describe his task as "rationalizing gameplay decisions with science and fact". BioWare not only went away from using lore as the building block. They shifted from story -> game design as a pre-planning process to 'what we want to play' -> 'how we explain that gameplay with story and lore'.

And on the upside gameplay is generally way more fun. I can just sit back and turn my brain off. Now, about that downside...

*Half a year later.

Weren't they a novel thing?

They should've probably made the ODSY Drive seem like a pipe dream or vapourware, a promised solution to the intergalaxy travel issue that the Initiative hid away from revealing to the galaxy, thus making everyone think they were bullshitting. Either that or just decided that Andromeda had Mass Relays too and use some unique Relay to send them there, damaging it in the process. Or... well, they could've done a lot of things, but they didn't. At one point there were mentions of things called phase gates linked to the Remnant. Might have been better if it had turned out there were remnant ruins in the MW and that's where the tech for the drive (and the ambition to go to Andromeda) came from.

I think the underlying problem was always EA. I like Mike Gamble for example but I don't think he would've been hired if it wasn't for the EA aquisition and he has a pretty integral role as the primary producer but the issue is he pushes for "cool" at almost every turn. Thankfully he's a smart guy and it seems he understands the story too but one of the Stormwaltz posts claimed that the lore-breaking additions like not wearing helmets in space in ME2 and probably also the need to "reload a gun with a clip" (my guess) came from the producer allowing the non-writing staff to do what they felt like. I don't know how BioWare operated back when they were "BioWare Corp" and people should also remember that in ME1 they had Microsoft as publishers who are also pretty influential on a studio-level same as EA but in a different kind of way. However, I think BioWare corp did not rely as much on producers and middle-men as EA does and that's why you get so much more rule of cool.

As long as we're talking flawed premises, the whole concept of having to leave the galaxy in order to stay hidden is borderline idiotic. OK, our chimp brains can't intuitively grasp the scale of interstellar space, but that's why you use thinking rather than instinct.

I don't know really, myself.

The only big complaint I have about the MEA is that it's the biggest criminal of the series yet, of deciding to just add new things without previous reference, hint, or easy narrative room. But the stuff itself is basically within bounds.
But I'm also not a physics nerd that could pick everything apart. But I also think anyone being a *total* physics nerd about Mass Effect, even the 'HARD SCIFI' ME1, needs to give their head a shake. It was also space opera and still retains elements of that.

Anyway, I think they made enough narrative room, even if barely.

Andromeda Initiative? Sorry but 100k people of a civilized population of trillions leaving on a fool's run to another galaxy is, while ridiculous not to note in previous material (thus my comments previous), quite fine to happen. It's not that many ships, they're not actually that big, and building them is ambitious but something easily that could have been only on the newsfeed for Shepard because he never went to Earth ME1-ME2.
We also should take things like Cerberus Network News as a hint that Bioware CAN allow lots of other things to happen in this galaxy that aren't only Shepard saving it. Hey maybe an asari world made a special discovery that changes the understanding of biotics as we know it, to the point of crazy Green Lantern powers? Maybe! Maybe! But then the Reapers attack . Okay, so now what? Well a future game could totally make this happen, 'retcon'. This is stuff that depending on circumstances, would indeed just be the newsfeed for almost everyone in the galaxy.

ODSY drives? Yeah they're problematic, but not very. 
1) They're not that super special. Technically, Bioware could go 'prototype' about anything, but it would surely be too much to say there's a drive that could cross galaxies within weeks or whatever. But this wasn't weeks, but centuries. I'm aware people still did the math and projected it as straining the lore. Cool, but I don't care. Sometimes its actually okay to have a prototype drive that can successfully do a long voyage.
2) The Ai is still mysterious. We don't fully know what supplies it, where they get all their tech and insights from, and it appears most to almost all of its participants are in the dark about that as well, with Jien as the PR face of it all. I am and always have been willing to give Bioware multiple games to flesh this matter out, prospectively including the development of the ODSY.
3) Generally speaking, most of the galaxy in their daily lives would not be fixated to the news that a long distance drive is being tested (and that's what Ai worryingly was - a test of many working-model experiments). It would be very meaningful to future decades and centuries of galactic development, but otherwise rather specialized news.


Now, could the galaxy have shuttled/arked people out during the invasion? No. The invasion was months until the end (less than a year?) and there's no intention to use resources that could go war/Crucible towards making a newly working Ark, especially as the point is the Ai was secretive about their level of development (with the SAM stuff as one hint about that).

All that happened was that the Liara line of 'it could be easy for a ship to get lost out there' in ME3 to have a potentially new meaning; that she's not just hoping for a stray ship of many people to repopulate somewhere away from the Reapers, nor expressing a basic escapism before some final battle, but she could be having hope that at least one Ark to find a home for the organics of the galaxy.
Shepard may be in our control 99%+ of the time, but in-universe he sleeps (without nightmare?), reads reports, is updated on news, etc. While it may be jarring to us players, it wouldn't actually be out of bounds that Shepard scrolled through ANN and learned of the Ai and that's it. "But it changes the whole context of the RP!" - Bioware hasn't top prioritized that in forever.