Hm... as a player, I don't like most of your card ideas, sorry.
I'll try to state why as precisely as possible.
I hope I'm not treading too much into Mystery Parfait's territory here by analyzing these cards, but it's good practice for creating rules for my own (video) game, so I can't let this chance pass by. xD;
Disclaimer: All of these statements are my own opinion. Even if I say "this is bad", read it as "I think it's bad". Even though this should be obvious, I feel like I should make this clear.
Hakurei Purification Rod:
I would (almost) never discard a card to be able to use another attack card.
Due to the card limit of 4, under normal circumstances, you have 6 cards at most in your hand in any given turn, usually less.
One card is spent for attacking (leaving you at 5 or less). Usually, you have a usable card in your hand (an Item card, an Invocation card, another Action card) (4 cards). If you've just played a Power, you can attack again. Alternatively, assume you're playing another Action card now. (3 cards left).
Now you want to leave some cards in hand to pretend you can dodge enemy attacks; heck, dodge cards are too valuable to burn no matter what. Also, you want to be capable of attacking in LATER turns, too.
So really, I would never spend my last cards so I can attack once more, leaving me at 1 card and as an easy target to pick up by any other player.
Also, this example was done with a hand of 6 cards. If you have less cards, the purification rod becomes even less useful.
As for discarding a card to turn your attack into a Seal Away... it's useful, but I don't know, I just don't like it when thinking of the person on the receiving end.
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Sword of Hisou:
Read: Discard a card to get a (semi-)random effect.
The randomness makes the life gain viable, winter is just unfun for the player on the receiving end.
But this card is at least more useful than the Hakurei Purification Rod, IMO.
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Full Power:
Even if you only put this card a single time in the entire deck, it is too powerful.
It can swing the entire game in such a way that it's not even funny.
Suddenly being able to attack three more times can potentially win you the game out of nothing. Given that you have the necessary attack cards for it.
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Tengu's Fan:
Reads: Once per round, be Aya with more range and distance.
In general, I don't like permanent cards that are like character's abilities, just weaker. Because, since they are permanent, you BECOME said character (with a limit), making this character less unique.
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Sacrificial Doll:
Terribly worded. It's basically "Once per attack, you may discard a card from your hand to either negate its damage or to not discard a Powerup card for taking damage."
Meh, could have worded it better, too, but whatever.
I REALLY don't like this card, as it's another PERMANENT card that basically makes you Aya. Except that you can still lose your Powerups upon negating damage, but instead, you can discard ANY card in your hand. AND you can use it on any attack, not just Danmaku cards.
Also, in general, Danmaku!! games are a little on the long side already, and cards like these here, that prevent damage (or let you regain health), only help to make the game even longer, which is something you REALLY want to avoid.
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Swallow's Cowrie Shell:
What I said above. There's a reason there are only two One Ups, and only one character with the ability to heal. Well, two if you count Tenshi, but in her case, it's more of a safety net in case her Spell Card fails.
Even if you limit it to once per round (as you did), regaining life by burning most likely useless cards is too powerful and just makes the game drag on longer than it should.
Also, "discard this card FROM PLAY"?! I really wouldn't want to introduce a mechanic for one card in the entire game; especially if it's a game where every player should have equal chance of getting a certain card.
But removing this card from play, it basically means "Haha, I got saved, you you can't get saved by this card cause it's gone now! Sucks to be you, guys!" *dies the following attack anyway*
This scenario is just not fun.
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Robe of the Fire Rat:
You really like the Trashing mechanic, don't you?
I don't, at least when it's overused. Which it really becomes if all your cards were to be in the game. xD;
My reason is, because Items show a certain progression in the game. People with more items are more powerful. But by having too many cards that trash items, it becomes incredibly tough to hold onto these items, because EVERYTHING can destroy them.
Regarding the counter part of the fire robe... it's interesting, but I don't particularly like it as something so powerful should not be a) coming for free, even if it is b) unreliable, thus barely even useful. And when it hits, it mostly feels cheap. Also, I just realized that it is actual LIFE LOSS and not just an attack, which makes it even cheaper, as you can't really play around it... unless you use one of the many "trash an item of your choosing" cards you have introduced.
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Stop the Lunar Invasion:
This is basically a reversed Fairy Wars. And that's why it's bad.
Fairy Wars makes you discard a (danmaku) card so you won't lose one life at the beginning of your turn. If you don't/ can't, it speeds up the game.
With your incident, it just helps prolong the game, and for a short time, creates a stalemate in which "only" your active hand size is reduced.
Again, cards that make the game last even longer are something to avoid, as the games can take rather long with enough people already.
Sorry for being so harsh on your cards; they all have interesting ideas, but I just think they don't really work out in this game.
Thankfully, I'm not a dev of this game, so who knows, maybe Moogs likes them or knows ways to make these cards work.