The details you note have often been seen as a controversial part of the narrative. In response to your first question, several possibilities exist. The demons, who can do nothing without God’s permission, know they have been bested (see Mark 5:13). Perhaps they asked to be put into the pigs so they would have a bodily home for their evil activity and avoid being sent into the Abyss (place of torment). Or, perhaps, they wanted to continue their destruction, in the case of the pigs, knowing that would make trouble for Jesus. Demons are always bent on creating chaos.
The greater question is, as you note, why Jesus assented to this plan. After all, it does involve destruction of property and the livelihood of the pigs’ owners. Here is where we see the love of God for individuals. We have to remember that the point of the story is not to destroy the demons but to deliver the demonized man from their power (Mark 5:19–10; Luke 8:39). As one commentator has noted, by sending the demons into the pigs, Jesus was giving proof that the demons had left the man, which was a profound gesture of mercy. When the people in the area saw those pig corpses floating in the lake and the man clothed and sane, no one could deny what had happened. More significantly, the man who was delivered, in the most dramatic deliverance given us in Scripture, would know that those demons were gone for good and feel supreme relief.