I watched the replay, BT. About the scoring, you don't keep your spell points high enough. In fact, you do some strange things sometimes which cause it to reset. The first is timing the enemies. Some good examples of it at the starts of stages 5 and 7. You seem to shoot a few fairies, then wait too long before shooting the next group. I don't know what to say about how you
should time it, since it's very situational, but I can recommend a possible way to practice them. Try to play the first stage without ever letting the spell points reset. Then watch the replay after and see which parts went wrong. With some practice at that you should be able to do it easily, and it helps learn how to use the fairies most effectively, not just for scoring but to get rid of bullets and keep yourself alive (which is the same as scoring but whatever). If I can point out a particular example:

I think you had a good opportunity here that you passed up. If you had shot the blue fairy there leading the others, it would have made the whole right side of the screen much safer. Instead you went down to the right and charged a spell, letting the fairies pass by, and a bullet wall descended upon you. Once you're earning all of the extends, I think identifying chances like that are what you need to do, since it's especially needed against Eiki.
You also sometimes charge up a spell then hold on to it for a while. There's no reason to do that, since you're defenseless while holding the spell, and your spell points of course reset. You also use level 3 spells sometimes, which I don't think should ever be done.
Another, less significant, thing I can point out is once in stage 9, when Lily appeared, you charged a spell then sat in front of her for a while before using it, presumably to cancel the bullets once she fired. If you had just spammed lasers at her instead she would quickly explode and drop an item, and you wouldn't have to lose a spell to her.
About what Seppo Hovi said about spamming level 2's against Eiki, I think I have to question it. It's good in many cases since you recharge quickly once you get it going, but Eiki is particularly dangerous if you do that, since the bullets you could normally reflect between spell uses (by shooting a few fairies) will usually have hot dogs fired along with them, which the fairies won't reflect, so it's very hard to create a situation where you can recharge the spells as quickly as you use them, which is what I think Seppo was referring to. You'll end up spamming spells anyway of course, but try to keep them for when you need them to survive.
I'm not sure if anything I said will really be that helpful, and do keep in mind that I'm not certain of anything about this game, since I still don't understand how it works. What I've said is just what I think I know.