1. It's used in a ton of web applications. It's slightly less popular than in the past due to the influx of frameworks like Rails and Django, but a lot of major web software (Wordpress, Drupal, Joomla, MediaWiki, phpBB) still uses it.
2. People tend to write very insecure PHP code, especially when they fail to use a framework. Again, this is slightly less true now than it was in the past. However, it's very common to see bad practices like:
- SQL queries generated via string concatenation
- Output escaping done manually, on a per-element basis, rather than in an automatic, context-sensitive manner.
- File upload scripts that let you upload PHP files, or file download scripts that accept a filename but don't sanitize against directory traversal attacks.
tptacek has a list of books on Amazon, linked to from his news.yc profile, which cover a wide range of application security topics (http://amzn.to/cthr46). I own The Art of Software Security Assessment and The Web Application Hacker's Handbook and I can vouch for them as quality resources, although I'm not sure how accessible they would be for a beginner.
In terms of a more practical introduction, Google Gruyere is an application deliberately built with security vulnerabilities for the purposes of learning (http://google-gruyere.appspot.com/). There are plenty of other projects along those lines: WebGoat is another good example.