I originally came to Poland to teach those guys and can assure you they ant that well thought of by the rest of the army for very good reason.
Sure you did, you're also an astronaut and and a superhero, got any more imaginary life tales to share?
So back then if you served outside of Warsaw you wouldn't get in?
Correct, still correct, the soldiers are drawn from units in or around Warsaw.
Would this be like the equivalent of the Household Cavalry in Poland?
The battalion itself consists of several detachments, the salute platoon (the guys who do the shoot in the air) several guard companies and a mounted company, the mounted company is the exact equivalent of various household and guard regiments in other countries like UK.
In a ceremony like the one above, would they try to have representatives from allover the country to be represented on parade? Or would these be primarily soldiers from the Warsaw garrison, if not, How would they decide on who gets to go on parade?
I didnt make it clear, the soldiers of the representatvie battalion are garrisoned in Warsaw hence you have to serve in the general area for convenience sake, privately you can live in Gdańsk or Kraków or wherever but you have to serve in Warsaw.
As for all over country, every polish division has its representative component, not all the same but representative battalion is the national level representative unit existing for the express purpose of well... presenting.
All other representative units are dudes who serve as regular grunts every other day.