Q: Can I not manage or delete and iMessage conversation that I started?
If I create a group message via iMessage shouldn't I be able to either delete the message (making it impossible for the conversation to continue) or remove individuals from the group message?
Nope, because everyone has equal participation. The only way to exclude someone is by making a new group chat without including the person(s) you don't want. To delete the chat, you essentially have to delete it off each participants device(s).