Heuristic argument for Weight decay and regularization
Perhaps I can answer the first and second one:

(1)According to (93) on his book:
$w \rightarrow w=\left(1-\frac{\eta \lambda}{n}\right) w -\frac{\eta}{m}
  \sum_x \frac{\partial C_x}{\partial w}$, 
there is an item $(1-\frac{\eta \lambda}{n})$on the weight, so weights will shrink every epoch. As weights were random chose at the beginning, it seems reasonable that the changes(the item $\frac{\eta}{m}\sum_x\frac{\partial C_x}{\partial w}$) will be chaotic on first epoch. Maybe that is why the weight decay will dominate the first epoch.
And there is another explanation here, which may be helpful.

(2)At each epoch, the item $(1-\frac{\eta \lambda}{n})$ will be multiplied $\frac{n}{m} $times, where $n$ is the number of training data, $m$ is the size of minibatch. So after each epoch, the weight will decay by a factor of$(1-\frac{\eta \lambda}{n})^\frac{n}{m}$. According to the definition of $e$:$e=\lim_{n\to \infty}(1+\frac{1}{n})^n$, lets change the format a little bit:

$(1-\frac{\eta \lambda}{n})^\frac{n}{m}=[(1-\frac{\eta \lambda}{n})^{-\frac{n}{\eta \lambda}}]^{-\frac{\eta \lambda}{m}}$

As you can see, when $\eta \lambda \ll n$,  $(1-\frac{\eta \lambda}{n})^{-\frac{n}{\eta \lambda}} \approx e$.Then we can come to the conclusion that provided $ηλ≪n$ the weights will decay by a factor of $exp(−ηλ/m)$ per epoch.

(3)I have been through this for two days and have no idea about it,but I think it should be related to the formula(85):

$\begin{eqnarray} C = -\frac{1}{n} \sum_{xj} \left[ y_j \ln a^L_j+(1-y_j) \ln
(1-a^L_j)\right] + \frac{\lambda}{2n} \sum_w w^2.
\end{eqnarray}$

where the weights were summed on last item.