feminine/masculine/neuter - Polish Grammar Question

I'm teaching myself Polish and I have a question about the change of adjectives. In this case, trudny.

1st sentence: Nauka polskiego jest trudna, studying Polish is difficult.
2nd sentence: Litery ż albo ź są bardzo trudne, letters ż and ź are very hard.
3rd sentence: Polski jest trudny, Polish is difficult.

My first question from the 1st sentence is: does nauka turn polski to polskiego and is that why it has changed to the feminine trudna?

My second question is (about the 2nd sentence): is litery masculine and is that why it is trudne?

My last question is (about the 3rd sentence): is polski neuter and is that why trudny is used?

Thank you.

@Sophaloaf

The answer for the first and third is the same. There is a word that is not present but is understood, in this case "język".

Nauka (języka) polskiego jest trudna

The study of (the) Polish (language) is difficult. "Nauka" is feminine nominative, and "trudna" agrees with it, "Jezyka" is masculine genitive, and "polskiego" agrees with it.

(Język) polski jest trudny.

(The) Polish (language) is difficult. "Język" is masculine nominative, and both "polski" and "trudny" agree with it,

As for the second sentence, you are confused because the ending for the nominative neuter singular and the non-virile plural are both "e", "Litera" is feminine, but "litery" is plural, and since it is not virile, or masculine personal, it takes the nominative plural non-virile ending, "e", which just happens to look like the nominative singular neuter ending "e". So "trudne" agrees with "litery".

Not always so transparent to determine gender in Polish, as it has no articles like in French or German etc., and so the "sex" so to speak of a noun must always be determined by their endings, e.g. "-o" nouns such as "oko", "okno", "dziecko" etc. will ALWAYS be neuter, while some nouns ending in "-iedź" for instance, must be feminine (odpowiedź = answer) or masculine (niedźwiedź =bear), although I've yet to encounter such an ending in the neuter:-) "ość" nouns will always be feminine and, again, masculine nouns show more variety.

More or less, gender must be learned by example, each noun at a time!

...although there's always MASCULINE "gość" just to throw things even further out of kilter, not contradicting what I posted before, because " -ość" as a purely FEMININE suffix, e.g. "miłOŚĆ", "godnÓŚĆ", "wolnOŚĆ" etc. are nouns representing an abstract state, therefore, are ALWAYS going to be feminine:-) But then, what about feminine "kość".....

Motto of the saga: Just learn 'em individually by heart and don't necessarily ask "why"!