"Ta kurtka nie jest zielona."
Translation:This jacket is not green.
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It's not that negation makes absolutely everything change into genitive. For example, a sentence with 'być' stays as it was: Ta kurtka jest zielona --> Ta kurtka nie jest zielona; Ja jestem nauczycielem --> Ja nie jestem nauczycielem, etc.
The most important example of a situation with negation=genitive, are sentences with 'mieć': Ja mam komputer --> Ja nie mam komputera, On ma dziewczynę --> On nie ma dziewczyny, etc. Accusative turns into genitive here. A lot of verbs have this feature of taking genitive when negated: Ja oglądam film --> Ja nie oglądam filmu, On gotuje obiad --> On nie gotuje obiadu... as a native, I don't necessarily know the rules, so it's hard for me to tell how wide this one is - just remember it's definitely not ALWAYS like that.
Maybe try to say them in your head throughout the day as you notice different colors around you.
I remember the rule for a sentence like this as: the complement of a naming phrase using the verb 'to be / być ' is in the nomanitive case. The complement of the verb is, in effect, an adjectve of the subject rather than being accusative object of a transitive verb (i.e. a verb with a direct object) therefore the complement is also nomanitive to agree with the phrase's subject.
No. You cannot use the 'to' construction if it's followed by just an adjective, it's like saying "This coat = green".