"Die weiße Katze und die weiße Blume.
How do you know if it is weiße or weißer? Does this have something to do with the gender of the noun?
Yes, and with whether there is ein/eine/einer/einem/einen or der/die/das/des/dem/den in front of it.
Since blum is single and blume is plural
I don't know which language that might be true in, but in (standard) German, the singular for "flower" is Blume (capital B at the beginning, -e at the end) and its plural is Blumen (capital B, -en).
Checking Wikipedia, it says that in Hunsrick and in Pennsylvania Dutch, we have Blumm, pl. Blumme, and in Afrikaans, it's blom, pl. blomme; are you perhaps influenced by some other Germanic language than Standard German?