So MJs believe Jesus was sinless and yet not God. Do they believe that he died for the world or only for Israel?
As I said, most MJs (who are usually financially backed by Evangelical groups) DO consider Jesus to be G-d, despite the fact that it's not Kosher to do so.
As for whether he died for the world or Israel, he died initially for Israel, he specifically said
"I Have only come for the Lost sheep of the House of Israel"
There's only so many ways you can interpret that.
And he told his Disciples to initially stay completely away from the gentiles. For a gentile to become part of the Church, they must become grafts to the tree, which means they must act like us, not us act like them. In other words, they must adopt the Torah and become like Jews. This is where the big controversy with Paulinism comes in, which was essentially not a major problem until around Marcion's time, but the controversy with Paul does have roots that go back to the pre-70 A.D. era.
Many MJs, like Zardoz here and myself, reject Paul's teachings and apostleship, and that is a very controversial subject. Most MJs are basically Evangelicals who obey the Law, many consider Paul to be completely pro-Jewish, and we all agree that obedience to the Law is a necessary minimum to maintain or earn the state of "being saved", for more questions, you can try the Messianic DIR, Zardoz can help provide some answers there as well. The initial church was completely Jewish and was but a Sect of Judaism.