The bold is critical here. Why is that kind of thing excusable there but not elsewhere?
That is a very fair question. It will be somewhat subjective in the sense that one person's Reasonable Suspension of Disbelief might stretch farther than another person's. I would say it depends on what we are being asked to accept. I think we tend to give more leeway to mind powers than we do things that are supposed to be based on technology, for one. I don't see the "essence of being a prothean" being given to Shepard any differently than I see the Asari mind melding in the first place. It's just passing knowledge from one mind to another. The biggest stretch for me with the Thorian is that it gained the info from Prothean fertilizer as opposed to observation or data archives.
It may also be that we are more likely to let a handwave slide than a really bad explanation. It also has to do with the level of detail given. Lazarus would have been a lot easier to swallow had they not showed Shepard's body burning up from atmospheric reentry.
Mass Effect as an IP was already "set up" at that point, though, and the Thorian marked the intro and extinction of a species that could do the things it did.
They could go any number of implausible alien directions with how to get to Andromeda, and it wouldn't really be any different than the Cipher or Lazarus.
You may have a point here. Most of the world building was done on that first trip to the Citadel. I still don't think the Cipher is as problematic as Lazarus but maybe that's just because the latter was so bad narratively.
As far as alien ways of transport, that's harder to do when it's the Milky Way races leaving. It would be far easier to get away with having that alien species come to the Milky Way. I could accept new technology or some sort of wormhole-like anomaly, but it would have to be presented well. I don't want a repeat of the Crucible where it just happened to be found at just the right time in a place it should have been found long ago.
Eh, Shepard's death was responsible for the forced Cerberus cooperation, the loss of Shepard's wealth/gear/stuff and the breakup of the band, which was given a chance to rebound by Lazarus after a two-year jump. I loathe that plot device and what it did to the series, but it did actually serve a purpose in ME2's excuse for a plot ... and not one too far removed from Shepard being forced to lug the beacon's filtered messages around in his/her brain.
The forced Cerberus cooperation was terrible. The gear/level reset didn't need a narrative excuse as games do that all the time. However it can be done better, like Metroid Prime, which starts you with a bunch of abilities and your suit gets damaged early on. Of course some players hate that kind of Abili-tease.
Breaking up the team could have been done as easily as having everyone go back to their own people because the mission is complete. The only thing that served a plot purpose was the connection to Cerberus and all they really did that mattered was get you EDI. The SR-2 doesn't do anything special other than not get totally destroyed by the Collector Cruiser. Any similar ship could have done so. And as we've discussed, Shepard's death didn't affect him/her at all. Characters barely acknowledge it and even get it wrong by claiming Shepard survived his ordeal.