Are they ways that God approved of?
SOme of them are; some aren't. Hosea was COMMANDED by god to take a certain prostitute as a wife.
The whole story (and book) of Ruth is basically one big love story. There was a LOT more to it than Boaz buying some land. In fact, Boaz was rich and already owned the land. Ruth and her mother-in-law (husband was dead) were poor peasants who went behind those reaping the fields and grabbed leftovers. Boaz saw them and felt compassion and told the workers to purposely leave some grain behind for them. Ruth eventually fell in love with Boaz yada, yada...
King David saw the wife of one of his soldiers bathing and wanted her. So, he had the husband killed and married her. This was definitely NOT approved of by god and his eldest son by the woman was killed by god as punishment.
It was (and still is) part of Jewish law that if your brother dies, you are required to care for his wife and family. In biblical times when multiple wives were common, this generally meant marrying your dead brother's wife.
It was accepted in biblical times to carry away attractive women in war as part of the spoils of war. Yes, they often married them and yes, god specifically OK'd the practice provided they converted away from idol worship and underwent "purification" rituals.
A few of the other methods mentioned are kind of hazy as to whether or not god approved but they did, in fact, happen in the Old Testament.