新たな/新しい? and how to use はず?
What is the difference between 新たな and 新しい?
Also, how do you use はず?

Question

Answer

新たな and 新しい both mean the same, "new", however 新たな is more formal.

About はず, it's like "ought, should, must, can, be sopposed to...depending on the sentence/situation. 
Here are examples: 
いま、9時半です。授業はもう始まっているはずです。(いま、くじはんです。じゅぎょうもうはじまっているはずです。) The class ought to have started / is supposed to have started / should have started / must have started.

彼はアメリカ人のはずです。(かれはアメリカじんのはずです。) He must be / can be American.

手紙は今日届くはずでした。(てがみはきょうとどくはずでした。) The letter was supposed to arrive today (but not yet).

I hope this was helpful.

Answer

新しい & 新た are the same. But I think 新た has somewhat more formal nuance.