I think the dead people appearing off-island weren't disguises taken on by the MIB. I think they actually were those people or, more specificially, souls of those who have difficulty moving on the island (the whispers). They were given permission by Jacob to communicate with those in the outside world as long as they serve the function of messengers on his part like delivering the message of telling the Oceanic Six to return to the island through Hurley.
On the subject of Claire, I also think the MIB imprisoned Claire within the whispers of the island while slowly corrupting her with his influence after taking her in Season 4. Either Jacob wasn't able to relinquish the MIB's hold over Claire among the whispers or he felt it wasn't time yet for her to rebel aganist it. But at some point, he was able to let her communicate with someone off-island and that someone was Kate. He wanted Claire to tell Kate not to bring Aaron to the island, either fearing for his safety or believing it wasn't time yet for Claire and Aaron to reunite.
On the subject of Claire, I also think the MIB imprisoned Claire within the whispers of the island while slowly corrupting her with his influence after taking her in Season 4. Either Jacob wasn't able to relinquish the MIB's hold over Claire among the whispers or he felt it wasn't time yet for her to rebel aganist it. But at some point, he was able to let her communicate with someone off-island and that someone was Kate. He wanted Claire to tell Kate not to bring Aaron to the island, either fearing for his safety or believing it wasn't time yet for Claire and Aaron to reunite.