It should give an article as choice. I had to say I have new cake. Which sounds horrible.
Sharing same semitic root with Arabic : حديث / حداثة ... Hadith / Hadatha. But with the meaning: recent / modernity.
That would go to the plural form to give a generality in Hebrew
יש לי מהעוגות החדשות
I have [of the] new cake[s]
Why not? I was told by some Israeli people that "UGAH" stands for any type of pie or cake. Isn't it true?
Any kind of sweet pie would be עוגה in Hebrew (though you could use, if you want to be more specific, פאי=pie as well). A savoury pie would be פשטידה.
I would have פשטידת תפוחים or פשטידת גזר. Maybe different places define differently.
It is always necessary that the adjective has the same gender ending that the noun right?
Not necessarily the same ending, but it needs to match the gender. There are feminine words that end with a consonant (like ציפור, bird) and there are masculine words that end with -ah (like לילה, night), but the adjective needs to match the gender, so
Good night = לילה טוב
A good bird = ציפור טובה