1. Is there a way to limit group creation to only one? I want a member to be able to create only one group.
Yes, within GJ > Config > Groups > General set "Limit" to 1.
2. I want the option to invite people to a group to be only available to the group owner only. Currently anybody on the group (owner and users) can invite other users. Is there a way to do that?
You can set the default for invite access within GJ > Config > Groups > Defaults and set "Invite Access" to "Group Owner" then set the dropdown next to it to "Hide". This will set the default for all future groups invite access to group owner and hide it so it can't be changed. Note defaults have no affect on existing groups, you need to edit and change their invite access manually.