Kagaribi: Nah, I said she was weak before, not shaky, since she's done that in other songs, like misterioso, but I said it kind of fits. Especially the second verse, where it's all quiet during her part in the beginning, which I really like.
I may not notice that, my fault...

. In fact, I don't like the way that she sounds 'weaker' in the second verse because it made the whole verse sounds weaker and not much connected with the other more energetic parts. I guess that it's a matter of preference then.
I hum the pre-chorus to believe and then I start humming the heavenly blue or to the beginning chorus. this is weird?
I'm with you..lol. Feel like that since Heavenly Blue. (I did mention it somewhere..., not sure whether in cpm or my facebook..lol, that I started humming 'Kirei na tsuki no akari ga...' when the chorus in HB starts..lol.) Heavenly Blue pre-chorus is so similar to TTB pre-chorus, and Believe pre-chorus is also similar to Heavenly Blue pre-chorus but not much similar to TTB pre-chorus.
I've listened to the full version already. I didn't hear that 'heavily-filtered' sound as much as I mentioned before...may be the problem lies in the anime clip that I watched..O_O.
I love the intro. After repeated the track for a while, I think that Wakana's second verse and chorus remind me a lot of Heavenly Blue. But I prefer the melody here to in Heavenly Blue. (May be the same way as some feel that Eternal Blue is so similar to PH and Toki no, but still prefer Eternal Blue..lol.) I feel like we haven't had this kind of long bridge in Kalafina song for a while... I think it's too long, not outstanding and quite forgettable bridge though.
In term of the arrangement, I didn't feel that Keiko's verse comes to sudden. It's weird to think that there is no instrumental gap between that two parts, but if I didn't keep that point in mind, it doesn't sound much weird. The whole song didn't much repetitive IMO.
Another thing that I've just thought of is the song 'Lapis'. As George pointed out, it means stone/jewel. Is it possible that it may be an insert song related to Rin?

Since Rin&Tohsaka family use jewels in their magic. (Just my guess...O_o.)