Is "czerwonego" used here instead of "czerwone" because 'dotykać' requires the genitive case?
Both the noun and the adjective describing it are used in Genitive. And yes, "dotykać" requiers Genitive.
How can we know wich verbs require genitive? Is there a rule or a list somewhere? I couldn't find any so far.
I think it has to do with the verb. For example, anything that is being drank always declines to Acc... pije wode,... anything that someone needs declines to genitive..... potrzebujesz kota
Why does dotykać require genitive? Is there some wider meaning behind this verb historically that requires such?
I know that's not really helpful, but I'm afraid there's usually no explanation, it's just how the language works and what it needs...
I must research if the other Slavic languages have a cognate of this word and if they also use the genitive, It's quite interesting :)