In an attempt to make an argument for why Meredith wanted the Circle annulled before Anders, I'll say this again.
The Templars have lost control of the Circle. That much is obvious, and regardless of why that's happened (Blood mage for a first enchanter or incompetence from the Templars), it's the situation. Mages are walking out of the Gallows, that well protected island, like it was nothing, and turning en masse into blood mages who are killing innocents. The Templar Order itself has been infiltrated by Blood Mages, so any dissent to Meredith's orders can be, in her mind, dismissed as blood magic. Demons are being summoned by the hundreds. Apostates roam freely in the city.
Lets not forget that the Codex entry for the Right of Annulment states (Italics added for emphasis)
Divine Galatea, responding to the catastrophe in Nevarra and hoping to
prevent further incidents, granted all the grand clerics of the Chantry
the power to purge a Circle entirely if they rule it irredeemable.
Meaning that a Circle does not have to be in the midst of a Ferelden Circle type situation for the Right to be considered.
Now, certainly, Meredith is a bit crazy to be asking for the Right of Annulment in this situation, which is why she gets rebuked twice. But, consider that Anders, in blowing up the Chantry, is attempting to strike the first blow in a mage revolt. The Circle has already shown itself to be outside Templar control, so to prevent a bloody revolt spreading, she orders the Templars to take down the biggest body of mages in Kirkwall.
As for not killing Anders, in my playthrough I saw that as a mark of respect towards Hawke. I believe she said something along the lines of 'He's your companion, you deal with him'. It made sense for my very pro-Templar Hawke (I spent all of Act 3 in Templar Armour!), but a lot less sense for any pro-Mage Hawke's out there. (Of course, my Hawke was 100% rivalry with Anders and very pro-Templar throughout, so I had to wonder why Anders was even my 'companion')