For general, let X be an abelian variety of dimension g. 
We say that X has 'purely additive reduction' at prime p if the dimension of the unipotent radical of the special fiber of the Neron Model of X is equal to g. 

I have two questions. 

- How do we practically check if a Jacobian of hyperelliptic curve has purely additive reduction at some place v. for example, Prof. Liu Qing pointed out (on the following post) Jacobian of $y^2 = x^{2g+1} + f$ $(f$ is uniformizing element of some prime $p$) has purely additive reduction at $p$

http://mathoverflow.net/questions/77959/can-we-always-find-a-curve-which-doesnt-have-semi-stable-reduction

But I don't know how to check it. 

- Let the Jacobian of $y^2 = x^{2g+1} + a_{2g}x^{2g} + ... + a_{0} $(defined over some number field $K$) has good reduction at $p$. And let $d$ be a uniformizing element of prime $p$. Then the Jacobian of $dy^2 = x^{2g+1} + a_{2g}x^{2g} + ... + a_{0} $ has purely additive reduction at $p$?. 
In other words, the Jacobian of $y^2 = x^{2g+1} + d^{1}a_{2g}x^{2g} + ... + d^{2g+1}a_{0} $ has purely additive reduction at $p$?
(those form has singular point at infinity when genus is larger than 1, so let's assume that we took those normalization before considering those Jacobian)

Thank you in advance!