@Ed_Miliband Don't worry! Thanks for your patience with me as I puzzle things out. I like to get everything exact.
I've been able to confirm that ברחבי is a preposition. The nekkudot is correct. After listening to it on Forvo I took out the sheva e in the transliteration.
https://forvo.com/search/ברחבי/
I'm still puzzling over the רחבי Pealim lists that in two forms, one an adjective construct, the other a noun.. https://www.pealim.com/search/?q=רחבי
I'm not entirely sure how Duolingo uses the word, the ones that came up in the search are only using it in the phrase בכל רחבי so maybe it isn't even taught on it's own, (Maybe there are more sentences I didn't see?). Still something that helps you learn the meaning of the phrase to have a entry for רחבי. I did a few lessons on Places but the snake is pretty hopeless at going through all the lessons in a skill, so I didn't find it.
I've gone with the information Pealim lists for adjective, masculine, construct. If someone has more information let me know.
I've done my best with these.
35 Places ברחבי around, across, through, throughout, all over, wide open space Preposition בְּרַחֲבֵי braḥavei
35 Places בכל רחבי all over, all around, all across, everywhere in, in all parts, throughout Plural Phrase בְּכָל רְחָבִי bkhol rḥavi
35 Places רחבי wide, vast, across Masculine Construct Plural Adjective רַחֲבֵי raḥavei
@EranBarLev If you have some time, would you let me know if I've got these right?