Is it strange to say "tego pisarza nowa książka"?
It is strange. Especially if you don't put any verb after it. But even in that case it is still strange.
Nowa książka tej pisarki? It can be female too right?
Of course, added now.
This is strange - it translates directly as "new book this writer's"? Ive not seen anything else in Polish like this, thus far
Well, so it's high time then ;)
Yes, in Polish it will also look this way: first you have the object owned and then the owner in Genitive.
Apart from simple using possessive pronouns, like "moja książka".
Well, that's like in Portuguese!
To jest nowa ksiazka pisarza. Why not?
To jest nowa ksiazka pisarza translates literally into 'This is (the) writer's new book'. The exercise asks you to translate an object (no verbs, such as jest needed)
It's not a sentence (it ends with a dot, but either it shouldn't, or we should just treat it as an answer to some question). It's just a phrase.