So the courts did find that he participated in an insurrection. But they also ruled that he had presidential immunity, and any prosecution would require an impeachment and trial in the senate. Basically, the courts said they didn’t have jurisdiction to prosecute him for it. They went “lol yeah he definitely did it, but we can’t punish him for it.” And the republicans haven’t actually challenged this. After all, why would they? They control congress, so they simply won’t try him for it in the senate.

But the 14th amendment doesn’t require a conviction. It only requires a sworn official to have violated their oath of office. Which includes participating in an insurrection. It doesn’t require a conviction or even prosecution; It only requires violating your oath of office.

The 14th amendment was written in the wake of the civil war, with the union looking to prevent confederates from holding office. The union feared that the confederates would attempt to seize power through the elections, even after the war was over. But they knew that taking every individual confederate to court would take way too long. It would also run counter to the reunification efforts, because no confederates would agree to rejoin the union if they knew it meant they’d be criminally prosecuted. So instead, the union circumvented the courts and simply barred anyone who violated an oath of office.

The ruling from the original court was that Trump engaged in an insurrection (but enjoys presidential immunity). The presidential immunity bit was then appealed to the Colorado supreme court, who overturned that. That is how we have arrived at (a) he was in an insurrection and (b) he does not qualify to be on the ballot. Trump and is team have never contested (a), so as far as this case goes there is no question about whether he engaged in the insurrection.

Yes to the first and no to the second, its complicated... And I am NOT a lawyer, so take this the way you would any response attempting to be helpful from the internet.

They are removing him due to section 3 of the 14th ammendment, which does not require one to be convicted of anything, just that you violated your oath of office and/or participated in an insurrection/rebellion. It does not really specify the legal mechanism for how this is supposed to works other than that they cant hold office anymore.

The wording is done this way due to southern states sending confederate politicians to washington during reconstruction. President Grant loosened the restriction in 1898 for the Spanish-American war, and since then its only been dusted off once in the 1920s.

Source: I went to the 14th ammendments Wikipedia page.

As for the second question, in theory it shoulden't give the GOP any ammo to turn around and do this to Biden. This is the reason its playing out slowly in the courts, the state AGs (just Colorado and Maine at this point) are waiting to see if that is a proper application of the ammendment. If the GOP did try turning around and doing this to Biden it would only take one federal judge to stop it. The supreme court could step in and clear this up quickly, but they appear to not want to be seen as a political body. So we wait.