See FAQ: Choosing the best doctype for your site [webmasterworld.com] and the reference links for info about doctypes and triggering layout modes. The Firefox Web Developer extension toolbar displays a tick icon to indicate rendering mode, along with lots of other useful features. Install it now!
Unless you have a specific reason for using XHTML, you should use HTML4.01 Trans or Strict. See Why most of us should NOT use XHTML [webmasterworld.com]
No, but HTML errors can cause layouts to go wonky (e.g. failing to close an element).
You should use the W3C validator to QA your markup, and fix any errors. It's the first step in debugging layout problems.
It's not difficult to write valid code once you've got the hang of it, and it will save you time and effort in the long run. You may also find this article useful Bulletproof HTML: 37 Steps to Perfect Markup [sitepoint.com]
(BTW: don't leave out the alt attribute where you don't need it, set it to blank: alt="")