Oh man, this is hilariously adorable. XD Great work.

Overall, this chapter and the previous chapter don't seem like they need to be separate; they would work well as a single chapter.

You could probably omit part of "the garage in our backyard that housed my dad's workshop"

I don't understand the simile "creaked like clockwork." Most clockwork doesn't creak, and "like clockwork" usually means running smoothly and reliably.

I think "mine and Matt's" should be "Matt's and my"

I like the foreshadowing of Keith's alien heritage, or at least a possible theory regarding it. I hope that comes back around when Pidge learns about it!

I think instead of "questioned" Matt should say "cared about," because to say they questions his age and intellect almost sounds like an insult.

I like the way you set up Katie's observation of alien radio signals, making her discovery in the show more believable.

I can buy Colleen and Katie agreeing that Shiro is handsome, but I don't buy Colleen teasing Katie about being in love with him. He is 9-10 years older than her, and she is so young now, Colleen wouldn't seriously encourage the idea.

I'm not sure if Katie having a crush on him is realistic. Maybe a celebrity or role model crush would make more sense than a romantic one. In the show she says she grew up hearing stories that made him out to be a legend, and that she always wanted to be a pilot, so she might want to get to know him or learn from him or impress him.

I like this premise, and the details you add to this offscreen moment, and the way Matt and Katie go at each other!

A few minor writing notes:
~ "there was a buzzing sound that came" could be simplified to "a buzzing sound came"
~ The D is missing from "and".
~ "fake punching" should be "fake punch"

Definitely want to see where this goes! Love stories that show Pidge's perspective on things! Do continue!