Traveling in the lower 48 I would not even consider replacing the spare. BUT. A trip to Alaska is a different story. Even thought the GY614s are great tires. I am not sure I would want to risk possibly having to use the spare for a long distance in remote areas. For peace of mind I would replace it. Throw the old tire in the bed of the truck in case you need a temporary replacement in the middle of nowhere.
For the second issue, I would pull the wheel again to make sure it still looks ok. Possibly something did not go back together exactly right, or you might have pushed grease thru the inner seal.