The quick answer is that the emails are broken up into parts:
In the component options under the Mail tab you had them set to hide so they weren't being displayed in either the Admin or Copy me email.
Below is an example received when the pats are set to display.
and if you are looking for a nice formatted version you can change the component option Email Format under the General tab to Rich HTML which will produce this:
I'm currently working on integrating the recently included custom filed system into the content plugin but for now you can display the older custom filed in the form (as you have already done) or you can switch to a module and then assign the new custom fields to it.
Let me know if you have any follow up questions.
Hi! I'm Steve the founder and head developer of CoalaWeb design studios. I'm an avid supporter of open source projects and the GPL license.