There's really no point. "Gensoukyou" is more proper. "Gensokyo" could have also worked, if less so, but only because of consistency (shortening the long vowels). "Gensokyou" is inconsistent, and thus is totally wrong.
She's mad at how Rinnosuke didn't utterly take advantage of her and I think it's a japanese way of venting anger... (I seen a Miyuki pic where she's mad at not being able to sing a song she wanted so soon after she slamed down her glasses)
She seems angry that all he did was pet her and I think she went full vent when she realized she liked it, so it seems like the hat thing is just an act of frustration or anger
Rinnosuke-san, I've run out of tea, so I'm taking some. You can put it on my tab!H... Hey! You two...!How long have you been there...?They're fawning over you.Oh, long enough.My, I think they're charming enough already!Well, I came here... because I thought you might need an outlet for your own fawning. ♥*giggle*Fawning, huh? If they want to fawn over me, they're gonna have to be a lot more charming about it...!A shrine maiden bearing the duty of protecting Gensoukyou and a witch who spares no effort... To think that the two of them feel not the slightest shame in coming to you to say whatever they want, depending on you, sometimes even bringing along their cooking, and killing their time listening to your stories... They are like children dropping by a small-time candy store.Kourin, this looks interesting, so I'll be borrowing it for life!So, what are you doing here?Me?He ended up petting me!Yukari-sama's snapped again!!I was happy!
I was happy, but!!*pet*Good grief! Time and time again, they not only barge in here making a ruckus, but they plunder my wares as well... What the heck are those girls thinking...?