Shouldn’t it be רָבוּעַ?
you can say it either way
Being born and raised here I’ve naturally heard both. But I think רבוע is the standard.
Shouldn't "We have a house of 200 meters square" be accepted?
Depends whether you mean 200m x 200m, i.e. it's a square with sides 200m, or 'two hundred metres squared' 200m^2 as a very widely used way of saying square metres. Admittedly the first is way too big for a house.
200 מ״ר got rejected, even though that’s normally how you’d write it.
יֵשׁ לָנוּ בַּיִת (של) מָאתַיִים מֶטְרִים מֵהַכִּיכָּר.
I know that there is a big difference between two hundred meters squared and two hundred square meters. But I'm confused about how to say each one correctly in Hebrew.
Generally, 'of' is going to be dropped. I have a 900 square foot house. The 'of' will sounds weird and oddly formal.
"that's two hundred square meters" was rejected but that's how you'd say this in English