Do you have a link/source on that? I haven't seen that, but if so, yes, it makes these questions more pressing.

Indeed. Sadly. People concerned with privacy and government overreach have been making noise about FISA for years, so if this incident could help to make the process less shady, that would be nice.

Yeah, I wouldn't buy that they did this by accident. It does show that the ongoing FBI investigation had enough substance that they didn't find it worth the risk/internal fuss to put an end to the surveillance. Of course, keep in mind that not only did Carter Page not join the Trump administration, but in fact he had left the campaign even before the FISA application (only just realized this myself - see my post below in the subthread with RT and AA). And you know how it goes in Trumpworld - once you're out of the team, Trump acts as if you were never really in his team and you never actually mattered.

It doesn't demonstrate that at all as far as I can see - like I said, it raises questions, sure, but it doesn't answer them.

I can't exactly claim to be an expert on intelligence gathering, but I know enough to realize that the process involves different categories of information with different degrees of reliability. The Trump partisans like to pretend that the dossier is about nothing but the scandalous sex stuff, but obviously there was a lot more to it, some parts more corroborated than others. When Steele decided to start sharing his information with the FBI, it was up to the FBI to corroborate and verify further. And yes, it definitely does matter whether he himself, having already a history as an accepted source of the FBI, made that decision or whether Clinton/the DNC ordered him to. If he made the decision himself without instructions from his client, then it matters a lot less who his client actually is - as in, the client paid him to gather the information, but he decided what to do with that information.

I'm not entirely sure who/what you refer to with the 'it was taken as fact', but if it refers to the FISA court, I'm pretty sure that those judges are aware that intelligence gathering or criminal investigations inevitably include degrees of certainty and uncertainty. Approving a wiretap on Carter Page doesn't mean at all that the judge believed every single thing said about him was a fact - just that the things said about him raised enough questions to make it worth the wiretap.

I'm not too sure how many checks and balances the FISA process ever actually had, so I'm not particularly shocked if it turns out that it wrongly violated the rights of an American citizen in this case as well. It's just that usually it's not this convenient for conservative partisans to be so critical about that process.

Edit:
Adding from a Politico article some quotes you may find interesting:

“As I have said repeatedly, I also remain 100 percent confident in Special Counsel Robert Mueller,” Rep. Trey Gowdy, an intel panel member, wrote on Twitter. “The contents of this memo do not — in any way — discredit his investigation.”

House Speaker Paul Ryan also remarked Thursday that he saw no connection between the memo and Rosenstein, even though it names him as having approved continued Foreign Intelligence Surveillance Act warrants for the communications of onetime Trump adviser Carter Page without disclosing that Democrats funded some of the research the FBI used to justify the snooping.

“This does not implicate the Mueller investigation. This does not implicate the DAG,” Ryan said, referring to the deputy attorney general. “This is about us holding the system accountable and reviewing whether or not FISA abuses occur.”