Learn Romanian: Decizia judecătoarei este clară.

This is the Genitive case, which shows possession (like the English apostrophe 's). For feminine nouns ending in -e like judecătoare (female judge), you form the definite genitive by replacing the final -e with the suffix -ei. So, judecătoare becomes judecătoarei (the judge's / of the judge).

Could I say Judecătoarei decizia este clară to match the English word order?

No, Romanian word order for possession is different. The thing that is owned (decizia) almost always comes before the owner (judecătoarei). It helps to translate it literally in your head as 'The decision of the judge'.

Does the adjective clară agree with decizia or judecătoarei?

It agrees with decizia (the decision). Decizia is a feminine singular noun, so the adjective must also be feminine singular (clară, instead of the masculine clar). The adjective always describes the core subject (the decision), not the owner.

How did decizie (decision) become decizia?

Decizie is a feminine singular noun. To say 'the decision', you add the definite article. For feminine nouns ending in -ie, the definite article is formed by changing the final -e to -a, making it decizia.