Keine's first SC -
replay. The third wave of attack is identical to the 1st, 4th is to the 2nd, and so on with 5th, 6th, etc.
If you need, I can give you a replay of timing out flying phoenix.
There is other way to deal with the 2nd phase of Posessed, but it's more risky if you don't do it right. You better stick with you method, it's the safest way already. Only one thing I'd like to advice - if you bomb it, don't move immediately (or just move donw a little bit), and only start to move down slowly when the bullets continue.
Hourai doll - your general idea is right but some details you need to know. When the stripes of bullets from left and right, you should move a little bit up or down (the safest way is to gaze those stripes), and if the stripe from top and bottom, you move left or right. (
Replay tried to time it out with Magic team but failed, dodged about 47 seconds, I think I could beat it if I shot)
And when you must bomb, try to use human side bombs (ie, Reimu and Marisa, I'm not very sure Sakuya and Youmu but I think it should be the same), they generally last longer than Youkai side and deal larger damage.
If you want to play on Magic team again, you may have a look of my replay in high score board for second half of the stage (the part between Keine and Mokou). You lost
one life and two bombs there, my method only requires one bomb.