[Math] Isometric isomorphism between $R^2$ and $R$

Question

Can someone help me solving the following problems?

1. $(\mathbb R^2,d_2)$ and $(\mathbb R, d_1)$, $d_2, d_1$ being the respective euclidean norms, are not isometric isomorphic, i.e. there is no distance preserving isomorphism between them.
2. Let $d$ be the restriction of the euclidean metric on $(-1,1) \times(-1,1).$ Find a metric $d':\mathbb R \times \mathbb R \to \mathbb R$ such that the spaces $((-1,1),d)$ and $(\mathbb R,d')$ are isometric isomorphic.

For 1.)
I thought it suffices to prove that if there was a isomorphism between those two, it wouldn't be distance preserving since it then also must be norm preserving which can't be injective since $||f(x)||_2 = ||x||_2 = ||f(-x)||_2$.

I don't know if that suffices or if it is even true. I would be glad if someone could prove me why they can't be isomorphic in the first place.

For 2.) I don't know what to do.

Answer 1

Hint: How many elements of $\Bbb R$ are of distance $1$ from $0$?