She has, but she sees no reason to use them as:
A. It would go against her principle to use the declaration as it explicitly states that a Villainess is the one using it.
B. She believes that she can do anything the Declaration can do anyways.
C. The power is too complex for her to use effectively.
She has access to all of regular Ssemouy and Seymour's knowledge. And I do mean all. This includes anything the two have forgotten. Rule of thumb is to basically consider her omniscient in everything pertaining to Ssemouy's lore. Emotions involving the memories are interpreted by her as purely facts, even if she would say otherwise.
I learned from the best (Certain VNs and JRPGs are really good at meta narratives) ?
You can, but do note that for the sake of the narrative, she is a "possibility" independent from time and dimensions, and she can thus occupy all possible timelines and dimensions where Ssemouy exists in. Otherwise she would be easily denied and erased by the Villainess' Declaration.
Answering your second question without spoiling things for everyone else is hard, but all I can say is that by all respects, they already do co-exist.
That turned out to be a fun coincidence, lol.
Her original existence was the very idea of a "Just Heroine", she clinged to Seymour, who is inherently selfish, therefore true justice to her is prioritizing the happiness of one individual over all others, since you are the only one capable of providing that individual happiness.
To her, she is the only path for Seymour and Matcha to achieve a 'true happy ending', whatever that may be. Whereas with Watcha's mission, his goal is plausibly achieved without him. The just thing to do would therefore be to prioritize Matcha's happiness by bringing him back into existence.
As for why Watcha's existence is not 'rightful'. For one, he came from the same place as her, so she knows how "wrong" the idea of him existing is. Two, she has bias(note that there is no malice behind this) against heroes, since in her mind self-sacrifice is their prerogative, go figure.
Also, she does have issues with eliminating him, else she would have simply attacked Watcha from the get go. She considers him eliminating himself out of own free will(even under duress) as the most 'ethical' method of going about what is necessary.
Yes, you could consider her a yandere on the same vein as Sato from Happy Sugar Life. Everything she does is justified by her fucked up logic in some way.
Sure. Here's a hint: It's not really meant to be solved by a human.
Yes, even those that have ceased to exist. She just has to imagine them living again. Though in the case of total erasure, you can argue that it wouldn't be true resurrection as what's brought back is Ssemouy's interpretation of them.
Ssemouy would interpret this literally, so yes, she can define the word "life" pretty easily.
She can travel even before the big bang, whatever that is
She could make it so that the big bang isn't even an existing theory.
She could redefine logical truths to make so universes wouldn't form in the first place, leaving everything as pure nothingness. And then create a universe anyways, because said logic can't dictate what she can do.
I think my previous responses answered this well enough, but her power can apply to pretty much everything as long as she can conceptualize it. Really, she is more plot device than actual character. Not really meant to be an 'alt form' to tap into like Seymour. Not to mention she convinces herself that she doesn't abuse her powers unless absolutely necessary.
Even though she actually abuses it on the regular, such as when she poured two types of tea from the same teapot, and using it to recite 10 thousand prayers daily while still keeping a schedule lax enough to waste several hours on games.
Huh, if what if Heroine Ssemouy put an absurd drawback like, "this can't actually kill and will cause the user to disappear from existence", and then used her powers to make the drawbacks trivial anyways. Would game balance nullify the rapier still? What if she infused a mundane object like a brick with her power to make it a sure-kill by some means? Would he be guarded against that?
Is game balance rigid or does it depend entirely on Watcha's perspective of "balance"?
Honestly, since both powers don't really have an effect by themself, it would just be a fistfight.