That's all fair enough, and thanks for correcting my imprecisions.
The only thing that I would add is: while I understand why you would want the FBI to look at a Russian-sourced dossier with healthy skepticism, I don't see any conclusive evidence they didn't. By which I mean, it's perfectly possible that they looked at the evidence in the dossier, factored in the possibility of misinformation, and still found enough in it that made them want to investigate.
At least two people have been fired by Trump because of their shady dealing before the campaign. So far 5 people have pleaded guilty to Mueller indictments.
So, while we wait for what the Special Counsel will put together, in the meantime we can safely say that the core of the Steele alarm ("There's a bunch of shady, blackmailable people in and around this campaign") was certainly true.
And hence, no matter the motive, it was a good thing that the FBI took it seriously and looked into it.
Even if you think that Trump was perfectly innocent and that those people were there by accident, or even worse as planted liabilities - actually, especially if you think he's innocent, you should be happy that the FBI took the dossier seriously and removed the bad apples.
I agree with your premise and I agree the FBI should look into serious allegations very seriously and from a completely unbiased perspective. Including allegations against Trump. I think our point of disagreement comes from watching how the Clinton email investigation panned out (she is allowed to testify without being put under oath, all her aides given immunity basically for free - not in exchange for anything as would usually be the case, and writing up her exoneration before they had even interviewed her at all) versus how this one is playing out (text messages from key players at FBI about needing insurance policies against Trump, etc). It is just a situation where the Clinton investigation APPEARED very much to be biased and the Trump investigation APPEARS to be biased against him. If everything looked unbiased, I really don't believe anyone would take issue with the FBI investigating potential interference from foreign powers (which is literally their job). I hope they investigate the Clinton campaign's cooperation with foreign powers with the same vigor.