She nods.  "Exactly.  But if he's got stuff to study I can definitely study it."

"Thanks. That'll be a huge help - I'm not really book smart at all."

"To complementary skillsets!" she says, raising an imaginary toast.

"To a well-rounded team!" She raises the toast back.

"Clink!"

She makes a rather impressive imitation of a clinking sound! It's still clearly made by human vocal cords, but just barely.

She giggles.  "You're good at that."

"Thanks!" she says in an exact imitation of Kaylee's voice (as she would've heard on a recording).

"Oh wow, that's really cool!"

"Took a while to get good at it, but I'm good at - the class of skills involved in acting?" she says in her own voice. "I can do characters, too."

"Maybe you should enter the talent show."

"Sounds fun!"

She'll let the conversation meander to lighter topics after that - talents and games and what to do for fun - until it's time to go home.

And she goes on another walk, slipping out after dark to lurk around alleyways, listening intently for trouble. 

The streets of Sunnydale are quiet, incandescent yellow-orange under the streetlamps, and the alleys are dark.

She keeps looking - ends up wandering into a park - and hears a scream.

Sounds like a time for her to test her Slayer speed!

...Is there an activation phrase for her superpowers or does she just start running - 

'Just start running' seems to work.

Wow she's fast.

She'll very quickly then come on a sight of a man being tormented by waves of dirt and sand rising from the park's ground. It smells like blood, but there's no injuries on the man - 

Yet.

There is a woman, however, maybe late teens or early twenties, standing at the apex of the sand.

Time to test SUPER FLYING KICK!

"Pick on someone your own size, asshole!" Nausicaa shouts as she launches herself at the sand woman (who looks very demonic and is almost certainly the one controlling the sand, Nausicaa really hopes she didn't get that wrong...).

Super flying kick connects, sending sand woman crashing back. Her sand collapses, and her prey makes a run for it.

She scowls at Nausicaa, baring her teeth. "If you're so eager to take his place - "

And she surges forwards, striking. She's strong and fast - 

But not Slayer fast - Slayer strong is another matter but Nausicaa's not letting her hit.

"Why attack him?" she demands.

"It proves my existence, that they fear me."

...If this is a metaphysical 'feeds on fear' thing Nausicaa is about to go off on entirely the wrong track, but she thinks it's a psychological thing - she recognizes that desperate look in the sand woman's eyes.

"Fear proves nothing. People fear all sorts of imagined monsters. But I know I exist. Because I protect people. Because I saved a girl earlier, and I saved that man, and I'll save everyone!" Punch punch kick dodge.

"Your philosophy is worth nothing. You are worth nothing!"

The woman lands a solid blow - sending Nausicaa flying.

Even with accelerated healing that'll bruise!

"I'm worth every hand I've stretched out into the darkness. Even if I die now... I'll be worth all the little ways I've made the world a better place."

"You know nothing! Nothing of pain, of misery, of hatred - I'll show you my hatred!"

"You think I don't know - "

The rest of the fight involves quite a bit of punching, and shouting, and earnest speeches about pain and suffering and doing better anyways, and then a bit of crying...