1) The sidebar displays fine for me here (Firefox 5, Chrome, IE9)
2) I think a plugin breaks this page. Maybe you're using a plugin or widget exclusively on it? I can't even validate the page with W3C: http://validator.w3.org/check?uri=http%3A%2F%2Fwww.chiemgaukicker.de%2Fneu-auf-chiemgaukicker-umfrage&charset=%28detect+automatically%29&doctype=Inline&group=0&user-agent=W3C_Validator%2F1.2
3) The line is part of the background image: http://www.chiemgaukicker.de/wp-content/themes/ThemeNewscast/newscast/images/skin3/bg.png - you can resize the image to your new header height (i.e. increase the image height to push the border down).
4) It seems that two different menus are currently in use so I assume you've problems to save sub menus? If yes please make sure that you're using Firefox or Chrome to edit the menu structure - around three days ago an user reported that the submenu items won't save if IE8/9 is used. The items just moved back to the left and displayed as main menu item. It's a WP3.2 bug and not related to the theme.
5) You can change the animation speed. Open up custom.js and search for:
slides: '>div', // wich element inside the container should serve as slide
animationSpeed: 900, // animation duration
autorotation: true, // autorotation true or false?
autorotationSpeed:3, // duration between autorotation switch in Seconds
easing: 'easeOutQuint', // animation easing, more options at the bottom of this file
event: 'mouseover', // event to focus a slide: mouseover or click
imageShadow:true, // should the image get a drop shadow to the left
imageShadowStrength:0.5, // how dark should that shadow be, recommended values: between 0.3 and 0.8, allowed between 0 and 1
fontOpacity: 1, // opacity for font, if set to 1 it will be stronger but most browsers got a small rendering glitch at 1
backgroundOpacity:0.8 // opacity for background
Increase the animationSpeed value (time in ms).