DiZ doesn't hate but dislikes Roxas possibly because how he believed that Nobodies are not meant to exist and cannot possibly feel, so he treats Roxas badly because he does not care for Roxas' wellbeing and dislikes him because he is one of the enemy. Though when Ansem the Wise died, he apologized for being cruel to Roxas.
No. After Xion tells Roxas to set the hearts free, Roxas goes to The World That Never Was, and is confronted by Riku, who defeats him by giving in to the darkness in his heart. Riku then gives Roxas to DiZ, so that DiZ may rewrite Roxas's memory. (this is also the beginning of Kingdom Hearts II)
Roxas is not stronger because Nobodies are only half a person. Namine says that in Kingdom Hearts II. And so does DiZ.
No he did not. Riku gave into the darkness and defeated Roxas so that he could give him to DiZ (Ansem) and have his memories of the organization erased.
Riku and DiZ captures Roxas and puts him in the virtual Twilight Town.
Yes DIZ did destroy kingdom hearts but not Xemnas that's why Sora needed to destroy him for the second reason.
It is explained in Kingdom Hearts 358/2 Days. *SPOILER* Riku captures Roxas after being defeated. However, he has to tap into the dark power in order to do so. That's why he looks like "Ansem" Riku/Ansem takes Roxas back to Diz and Roxas is place in a simulation Twilight Town while Namine works on Sora's memories, which she messed up in Kingdom Heart: Chain of Memories.
DiZ is revealed to be Ansem the Wise at the end of Kingdom Hearts 2, when he sacrifices his life in an attempt to destroy Kingdom Hearts.
In Kingdom Hearts 2, Roxas beats Axel in the DiZ's simulated Twilight Town, since Roxas then destroys the computer before returning to Sora. After that, Sora ends up in the real Twilight Town then uses the real, un-broken computer to teleport to the fake one with the broken computer.
Riku and RoxasIn Kingdom Hearts 2, Riku fought and beated Roxas and brought him to DiZ to erase his memory of being in Organization XIII and to replace it with another memory, a fake one of Roxas having grown up in Twlight Town.
In Kingdom Hearts 358/2 Days you can unlock Sora and Mickey as playable charecters. As of now, you cannot play as Diz.
*WARNING-SPOILERS*Towards the end of Kingdom Hearts 358/2 Days, after Xion is defeated by Roxas, she requests that he "stop Xemnas". Roxas unquestionably ventured to The World That Never Was. He was confronted by Riku who defeated him by giving in to the darkness in his heart. Riku gave him to DiZ to have Roxas's memories erased so that Sora can be fully restored.
Roxas is a Nobody who was created when Sora vanquished his heart using the Keyblade of People's Hearts at Hollow Bastion. In the process, Namine was born. Namine is a Nobody that is half of Kairi and half of Sora. Sora turned himself into a Heartless, and when anyone with a strong enough heart becomes a Heartless, the empty shell left behind is turned into a Nobody.*Spoilers*This Nobody, Roxas, was found by Organization XIII and used as a way to gather hearts, since Roxas had control over the Keyblade. After Roxas left the Organization, he was defeated and put unconscious by Riku who then gave Roxas to DiZ. DiZ put Roxas in a virtual town and hid him from the Organization so that he could become one with Sora once again. This is the prelude and beginning to Kingdom Hearts II.For more in-depth information, see the question "How does Kingdom Hearts 358 2 Days end?"