Here's a chart with the translation for all weather effects: Please let me know if I made any mistake (especially if it involves an effect useful for speedrunning)

This is an explanation of what affects the final spellcard of each boss. Also a translation of the Kanji that show up whenever you finish a boss' phase: Turns out that if you do really really badly you'll get some blue Kanji. I don't even know what it says I only saw it on some let's plays. I assume it'll do the same thing as the Kanji to the left on the image.

Translation of the results screen after clearing a stage (by Gesh86):

Also I'm gonna explain a certain mechanic in this game that apparently everyone fails to notice (I didn't know for the longest, and even the two Japanese runners of this game don't use it): You have 4 styles in this game. In each one you can equip a shot type and a spellcard, then you can switch between them as a shortcut (as opposed to going to the menu and switching your shot type every time you want something new). This style system is nothing new and you have it in plenty of other games. What's different is that your styles are charging. If you look at the top of the screen, you'll notice that a style you just used is fully black, and it slowly fills with a red color until it's red and blinking, meaning it's fully charged. I believe it takes 15 seconds for a style to charge. When you switch into a fully charged style, Tenshi gets this red aura around her for about 3 seconds. While that aura is up, ALL of your damage is increased by 25%. This means spellcards, shot types, melee, the sword, everything gets a damage boost. Most common use of this is to drop, for example, 4 of those bomb bullets I use a lot, and just before they blow up you switch styles, into a style that's charged. Each one of the bombs gets a 25% boost, which essentially means you got a free fifth bomb from all the added damage. You only unlock style charging on Stage 2. You can't use this on Reisen (not even in boss rush!). If you combine this with the fact that the bombs deal stupid amounts of damage (especially when you dash cancel them, to spam a bunch of them in a row), and the fact that if you dodge an enemy's attack they'll take extra damage while glowing red, you can deal an insane amount of damage.