Let $D=\{z \in \mathbb{C}: |z|<1\}$, then which of the following are true?

Question

Let $D=\{z \in \mathbb{C}: |z|<1\}$, then which of the following are true?

1. There exists a holomorphic function $f:D\to D$ with $f(0)=0$ and $f'(0)=2$.
2. There exists a holomorphic function $f:D\to D$ with $f(3/4)=3/4$ and $f'(2/3)=3/4$.
3. There exists a holomorphic function $f:D\to D$ with $f(3/4)=-3/4$ and $f'(3/4)=-3/4$.
4. There exists a holomorphic function $f:D\to D$ with $f(1/2)=-1/2$ and $f'(1/4)=1$.

Now for option $1$, I see that it is not true by Schwarz lemma. But I don't know how to decide the rest. Schwarz lemma says one more thing that if $|f(z)|=|z|$ then $f(z)=az$ where $|a|=1$. So $|f(3/4)|=|-3/4|=3/4$, is this going to help? How can I proceed further? Help needed please.

Edit: Ok I just found that this is a duplicate of this question, but I still appreciate some answers as I didn't properly understand the answer given.