Function Fields & Ring of regular functions

Question

From here - https://crypto.stanford.edu/pbc/notes/elliptic/funcfield.html

This leads us to define the ring of regular functions of $E$ to be

$K[E] = K[X,Y]/\langle f\rangle$

Its field of fractions $K(E)$ is called the field of rational functions of E

I find all the notations used here to be a little confusing.

1. When we say $E(K)$, it denotes an elliptic curve $E$ whose coordinates are in the field $K$ & when we say $E/L$ it means an elliptic curve $E$ whose equation coefficients are in $L$

I am struggling to understand here what $K[E]$ means as compared to say $E(K)$. The only thing I can think of is that this notation may be similar to $R[x]$ where $R$ is a ring of polynomials. So does $K[E]$ mean it's a ring of all elliptic curves? If so, what exactly is a ring of elliptic curves - how does a set of elliptic curves become a ring?

2. What is the meaning of the notation $K[X,Y]/\langle f\rangle$?

This notation usually means the ring of polynomials (of $X$,$Y$) quotiented by the ideal generated by $f$ - does it mean the same here?

3. What does "regular" mean in the phrase "ring of regular functions"?

4. What does field of fractions mean? What fractions are we talking about here?

5. What does "rational functions of $E$" mean here? I understand what is a ration function, but what is $E$ here - is $E$ a particular Elliptic Curve (i.e. defined by a particular equation)? Or is it some set of elliptic curves?