In the episode The Keeper Of Traken the planet Traken is so peaceful it lures evil creatures too it like moths to a flame and they become trapped there and begin to calcify.

The statue above is assumed to be one of these "Melkur" and the Trakenites take pity on such creatures and visit them hoping they will turn away from evil and eventually stop being statues.

In reality this particular one was one of The Master's Tardises which he has disguised as a calcifying creature to take over the power source of the planet (the reason why everyone is so nice) to regenerate his dying body.

"Having a stork on" is a typical Tom phrase it equates to "having a stiffy".

While we are talking Who here is a statue of Aggedor :