Genitive can be used for nouns denoting qualities, then it means 'having this quality'. For example:
- челове́к че́сти (a person of honour = a person having the quality 'honour' = a honourable person),
- слёзы ра́дости (tears of hapiness = happy tears).
It's also used with a phrase 'adjective + noun':
- ве́щь кра́сного цве́та (a thing of red colour; thing having the quality 'red colour'),
- же́нщина высо́кого ро́ста (a woman of tall stature = woman having the quality 'tall stature')
- цвето́к необыча́йной красоты́ (a flower of outstanding beauty = a very beautiful flower),
- челове́к огро́много профессионали́зма (a person of huge professionalism = a very professional person).
In this sentence, there's a nominal phrase 'adjective-like question word + noun' in genitive: «како́го цве́та». It's similar to «ве́щь кра́сного цве́та», but instead of «кра́сного» we have a question word «како́го». «Како́го» grammatically behaves like an adjective. So, we have a question about a quality, and that's why we use genitive.
Yes, you're right. Using genitive definitely sounds more formal (or poetic).
Дело is used about things people do, actions, business. You can't use де́ло when asking about colour because actions don't really have colours.