Generalising Plane Isometries to $\mathbb{R}^3$

Question

Firstly, I DO NOT WANT PROOFS OF ANY OF THESE THEOREMS, as I wish to prove them myself. However, I would like to know the correct generalizations to $\mathbb{R}^3$ of the following theorems:

1. An isometry on $\mathbb{R}^2$ that fixes three non-collinear points is the identity.
2. An isometry on $\mathbb{R}^2$ that fixes two points is a reflection or the identity.
3. An isometry on $\mathbb{R}^2$ that fixes exactly one point is a product of two reflections.
4. Every isometry on $\mathbb{R}^2$ is a product of at most three reflections.

Here are my thoughts so far:

1. An isometry on $\mathbb{R}^3$ that fixes four non-coplanar points is the identity.
2. An isometry on $\mathbb{R}^3$ that fixes three non-collinear points is a reflection or the identity.
3. Not so sure.
4. Every isometry on $\mathbb{R}^3$ is a product of at most four reflections.

Answer 1

I asked my lecturer today, and he said that the generalizations are as follows

1. An isometry on $\mathbb{R}^3$ that fixes four non-coplanar points, where no three are collinear, is the identity.
2. An isometry on $\mathbb{R}^3$ that fixes three non-collinear points is a reflection or the identity.
3. An isometry on $\mathbb{R}^3$ that fixes two points is a product of at most two reflections.
4. Every isometry on $\mathbb{R}^3$ is a product of at most four reflections.