We're not actually sure that Widmore faked the plane crash. Felix was delivering pictures to Widmore of the empty graves and the purchase order for the plane. These pictures are presumably the same pictures Mr. Friendly showed Michael. Could Mr. Friendly have killed Felix and taken the pictures, so Widmore would not be 100% sure that it was indeed Ben?
As for the other team, they could be working for Eloise. Given the fact that we know that Ben, Widmore, & Eloise were all in leadership roles on the island, there probably was a power struggle between them. Eloise lost out first, got banished (as she was not ever mentioned in the past week's episode flashback), then Widmore, then ultimately Ben. All 3 want to protect the island, but still want to use it for themselves. The big "war" everyone is speaking of, is the final struggle when Widmore, Ben, & Eloise ALL return to what they claim as theirs.