If you are changing only theme or template, make sure that your content is still the same with the meta and keywords. It might affect but slightly still.
Make sure all the page URLs are exactly the same, or do 301 redirects to the new pages. Try not to go to crazy with changing content all at once. Also, be sure the page titles and meta description remains the same.
yes as said above do change the content gradually and make sure the page urls are same like before other wise existing pages whaich are already indexed in the google will loose ranking and and will be eventually deindexed
if you are just changing a theme (e.g., in wordpress) you will be fine. If you are changing the URLs, make sure to do 301 redirects (can use redirection plugin)
Changing the design shouldn't affect SERP that much if at all unless the load time for your pages increases dramatically. The on-page SEO is what matters most. Don't mess with your metatags, titles, and keyword density and you should be fine. Of course you can always do a database backup and if it does affect your SERP, then you can always go back to how it was.
if you put all url, content and meta tags same as it was...then you will loose ranking but slightly.....but if you are going to make major changes, definitely you will loose ranking