Various replys:
Now THIS is sad.
132 attempts, and I STILL can't capture Light Sign "Halo of the Guze Kannon".
Why, Miko, why?
Given the spell card name, I guess that's on Normal. I find that it's really easy for me to pick out the yellow flashing bullets on Normal. If you dodge to the right of it every single time you see one, you should capture the card with minimal effort (or at least that's what I remember of it).
This doesn't work on Hard and above though :V. The yellow bullets veer too far away from Miko for you to be able to both hit her and get in that safe lane.
How do I capture Embers of Love (no. 172) and Philosopy of a Hated Person (no. 174)?
The former I can sort of capture 50% of the time but I get trapped a fair amount of times.
For Philosopy, mainly the last phase. I don't know what to do and run into bullet 
For Embers, you should always be under Koishi when she shoots the aimed hearts straight at you. She'll then fire a wave away from you, then repeat. Just repeat. It only really gets harrowing in the last few moments of the card, but for me at least, I couldn't capture it that consistently until I got a feel for how the bullets on the tail spawned.
For Philosophy of a Hated Person's last phase, it's basically just moving in a clockwise direction around the center of the screen, following Koishi around. To my eyes at least, it looks like the bullet walls are moving diagonally, but they're actually moving straight across, so you can dodge them by moving completely horizontally/vertically. Also note that if you do get caught by Koishi, staying in the center of a "square" is completely safe.
I am slaving away at doing my first extra stage, the logical choice being Imperishable Night. A couple of questions:
1. Keine's first and third spells. Is it better to be unfocused or focused while the spirals are firing? (it changes the speed)
2. Ikahasa's moon curse. I can sort of see a path by going to the left, but I have nowhere left to go when returning to the center. Is there a more suitable path to evade those rebounding knives?
3. Phoenix Rebirth: I need a foolproof way to misdirect the phoenixes.
4. Hollow Giant "Woo". Again, what kind of path is needed to properly misdirect the bullet sprays?
1. For her first spell, the familiars shoot two different static patterns that you can easily dodge before the aimed sprays. The safespot for the first wave is above the "E" in "Enemy" and I believe the safespot for the second wave is between the 'n' and the second 'e'. After most of the static bullets move past, just slowly stream. Repeat. For her third spell, the bullet walls are again completely static every single time. I dodge it by starting over the "E" and streaming to the right. The addition of the teal bullets in later waves is just a minor complication. Dodge them normally.
2. The path I use starts in the center, stays for 2 waves, then goes to the right, returns to the center, then right, then back again. It should finish the card off if you're using the border team. Moving to the right is better than moving to the left because the knives fire in a clockwise rotation, meaning that there is a huge hole to the right if they are aimed at the center. Knives will more or less always be coming at you from the left, so don't go that way.
3+4. I'm not too sure what Phoenix Rebirth is. In either case, you can see good techniques and explanations for most of the remaining spells from this Kefit video.
http://www.youtube.com/watch?v=tACAYUgYcBs. Do note that he's using solo Alice, which clears all of Mokou's cards in fairly fast time, so you may need to dodge for a while longer than he is. His paths are applicable for all teams though.
Ugh. I always have trouble with Remilia's first nonspell in EoSD on any difficulty, even Normal. I get to her with two lives or one (depending on whether or not I derp on Sakuya midboss nonspell (I always time it out because I don't want to deal with Eternal Meek.)) and that nonspell takes up all my lives. If I somehow make it with one left, I'll derp on Star of David. I curse that nonspell. DX
Remilia's first non-spell can be a bit tricky. The only advice I can really give based off of personal experience is to never ever ever try to dodge between a bubble bullet and the completely solid big bullets (like the kind fired during Star of David). I feel as though EoSD has weird bubble bullet hitboxes (or at least larger ones than the rest of the series), and it tends to throw me for a loop. For Star of David, basically sit at the bottom of the screen and dodge in between lasers/bullets.
Also one question mine, is normal that some stars does not explodes and shots a circle of bullets instead?
Yes, it's normal for you to see bullet circles. The entire array shoots in a big aimed "circle". I'm not too sure how to describe it, but if you watch a replay of the spell a few times you'll see what I mean.