Greetings Kdhamilton,
It is possible to forward individual messages from a conversation to a different iCloud account. See this article -
Send messages with your iPhone, iPad, or iPod touch - Apple Support
In particular the section titled How do I forward a message?
Regarding pictures and contacts, the easiest way to transfer these to a new account would be through a computer. Pictures you can import to the computer and then use the iCloud web interface to move them to your new iCloud account. See this article -
OS X Yosemite: Share photos and videos with your family
Contacts will be somewhat easier in that you can export them and import them as a whole rather than individual contacts. This article explains how to export contacts from iCloud -
iCloud: Export contact information as a vCard
This article explains how to import those contacts into your new account -
iCloud: Import a vCard
Thanks for using Apple Support Communities.
Be well,
Brett L