Learn Portuguese (Portugal): Vêm cá a casa e trazem um petisco? - Are you guys coming here to the house and bringing a snack?

Because the speaker is currently at the destination (the house). In Portuguese, vir is strictly used for movement towards the speaker's current location. If the speaker were meeting them at a different location, they would have to use ir.

Could I use levam instead of trazem for bringing the snack?

No. Trazer is used for transporting objects towards the speaker's current location, making it the perfect pair for vir. You use levar when taking an object away from your current location (which would pair with ir).

Why does the sentence use cá instead of aqui for 'here'?

While both mean 'here', cá is strongly preferred with verbs of motion to indicate movement towards the speaker, much like the old English word 'hither'. It also suggests a slightly broader space than aqui, fitting the idea of 'over here' at the house.

Why does it say a casa rather than para casa?