I want to start another website with the same contents as my current website, I just want to change the CSS sheet so it looks a little different. Will search engines be ok with this as the file name is the same as my current website apart from the domain. Thanks.....
No they will not be ok, the new website will not be indexed or banned because of the dublicate content, one of my clients did the same some time ago.
I wouldn't do it. Most search engines don't like duplicate content (read: websites) It is best to have different websites and different layouts.
When you have duplicate content.. search engines won't like it. i suggest you dont do it. put a different content on that other site, im sure that has more advantages.
For search engines purposes is a bad idea, but great for mirroring your main site if hosting downtime occurs.
You can attach more than one stylesheet to each website and allow the user to change it with a button or something. Not sure how it's done but if you ask in the css forum I'm sure you'll get plenty of help.