The caliph is someone who orders authority over Muslims.
The chief Muslim civil and religious ruler, regarded as the successor of Muhammad
How are they spreading Islam?
They're spreading Islam by going to near, and peaceful empires.
How does this spread of Islam compare to other ways other religions have spread?
It compares because, since all the religions we have learned, almost every religion was spread peacefully.
How does the spread of Islam after the death of Muhammad compare to how was spread during Muhammad's life?
It compares because when Muhammad was alive they were spreading the religion peacefully, but then when he died they were spreading the religion by conquest, or violently a totally different way they were when Muhammad was alive.