Affine Line over $\mathbb R$

I am reading "The Rising Sea" by Ravi Vakil. I have several question regarding section 3.2 .

1. We know $\operatorname{Spec}\mathbb{C}[x]$ looks like, and we can associate each maximal ideal to a complex number. But what about genric point?

2. What is the intuition behind the terminology: the elements of $\operatorname{Spec} A$ is points and elements of $A$ as functions?

3. And I don't know how this affine line over $\mathbb R$ looks, I know what is $\operatorname{Spec}\mathbb{R}[x]$.

please find the attachment for 3rd one.

Question 3