YES, how else would make him feel as if he had to constantly aduct peach? But he also wants to kill Mario to get rid of the the compatition. He's been noticing that peach has been showing much affection to peach when he rescues her. The answer is a defenet YES.
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If what the games show is any indication, it likely varies depending on Bowser's plot, although it generally involves her being kept in a cage. For example, in the first Super Mario Bros. game, she was simply kept in a chamber behind where Mario battles Bowser (the All-Star remake, though, shows her in a cage over lava), while in Paper Mario shows her kept in a room of her own castle, which was carried into space by Bowser.
Because Peach has a power to undo Bowser's spells. Bowser knows this so he kidnaps her.