electromagnetism - What is the physical meaning of the terms in the multipole expansion?

I have a few questions on multipole expansions and I have read about the topic in many places but could not find an answer to my questions, so please be patient with me.

The electrostatic potential due to an arbitrary charge distribution $\rho(\mathbf{r}')$ at a given point $\mathbf{r}$ is given (up to a factor of $1/4\pi\epsilon_0$) by

$$ V(\mathbf{r})=\int_{V'}\frac{\rho(\mathbf{r}')}{|\mathbf{r}-\mathbf{r}'|} dV'$$

In case where $r\gg r'$, $V(\mathbf{r})$ can be multipole expanded to give

$$V(\mathbf{r})=V(\mathbf{r})_\text{mon}+V(\mathbf{r})_\text{dip}+V(\mathbf{r})_\text{quad}+\cdots$$

where

\begin{align} V(\mathbf{r})_\text{mon}& =\frac{1}{r}\int_{V~`}\rho(\mathbf{r}') dV',\\ V(\mathbf{r})_\text{dip}&=\frac{1}{r^2}\int_{V~`}\rho(\mathbf{r}') ~\hat{\mathbf{r}}\cdot\mathbf{r}'dV', \\ V(\mathbf{r})_\text{quad}&=\frac{1}{r^3}\int_{V~`}\rho(\mathbf{r}') ~\left(3(\hat{\mathbf{r}}\cdot\mathbf{r}')^2-r'^2\right)dV', \end{align} and so on.

Now here are my questions:

1. 
   

   Is there an intuitive meaning of every one of these terms? For example, I can make sense of the monopole term in the following way: to the 1st approximation the charge distribution will look like a point charge sitting at the origin, which mathematically corresponds to what is called a monopole term, which is nothing but $Q/r$. Is this correct?

   
   


2. 
   

   Now what is the meaning of the dipole term? I know that the word dipole comes from having 2 opposite charges, and the potential due to that configuration, if the charges are aligned along the $z$ axis symmetrically say, goes like $\frac{\cos\theta}{r^2}$. But from the multipole expansion there is a nonzero dipole term even, say, in the case of a single charge sitting at some distance from the origin. Why is it called a dipole term then? Is there a way to make sense of this term in the same way I made sense of the monopole term?

   
   
   


3. 
   

   What is the intuitive meaning of the quadrupole term?

   
   


4. 
   

   Is the multipole expansion an expansion in powers of $1/r$ only? or of $\cos\theta$ too?

   
   


5. 
   

   Maybe this is not an independent question but I am wondering if there is something like a geometrical/pictorial meaning of every term in the multipole expansion.