What you have written sounds ok except for the Zn changing to black crystals. The Pb is plating out on the surface of the Zn and that is the reason for the change of color. The Zn isn't changing color. Here is an answer I gave in some detail to the same question that may help.
http://www.jiskha.com/display.cgi?id=1245515913
does this sound right for what happens with the zinc and lead nitrate reaction? could i add anything else?
The zinc displaces the lead. You can observe the lead preipitating on the zinc surface. The zinc changes to black crystals which dissolve in the water and there are lead crystals.
i hav a feeling that some of my answer is jumbled up. please correct me and give a more reasonable answer which is basic and not too complicated because I do not understand the 'precipitating' bit.
2 answers
colour less lead nitrate crystals are heated