He probably didn't track Kate but the tracksuits. He knows how his enemies move. Seeing them mobile and cornering someone in a car would have been enough for him to find Kate
In black market audition the guy said the costume was in Avengers custody. Kate wouldn't dig too much into it believing it's just Avengers business.
The LARP firefighter committed a crime. Imagine stealing something from a crime scene so you can role play.