In plural nouns and also adjectives which describe them are splitted into two categories masculine-personal (masculine nouns which name people) and non-masculine-personal (feminine, neuter and masculine nouns which don't name people - things and animals) "Parasol" (singular) is masculine but it is a thing so in plural it is non-masculine-personal. Moreover it is used in Accusative.

So the adjective "kolorowy" has to agree with a non-masculine-personal noun used in Accustaive case. Therefore you have to know the pattern in which adjective "kolorowy" is declined. Click on the text "decension of kolorowy" and then check plural -> other -> Accusative: https://en.wiktionary.org/wiki/kolorowy

umbrellas - plural
parasol ->parasole (plural not masculine or personal)
like-> lubią + Accusative
kolorowy -> plural non personal accusative -> kolorowe

Standard ending for adjectives in non-masculine-personal plural nominative/accusative/vocative.

Full ending table here: https://en.wikipedia.org/wiki/Polish_grammar#Adjectives

Kolorow mean colors. But colorowE means colorful

"parasol" and "parasolka" may be synonyms, although they don't have to.

"parasol" is a basic word for both an umbrella and a parasol (this one actually makes more sense etymologically), "parasolka" is definitely an umbrella, in theory it's a smaller one, rather for women. I personally wouldn't care for the last part, I am alright with the idea of carrying "parasolka" myself.

Yes, it does.