I can confirm that JIRA supports email notifications. The due date thing is odd though, by default you can set due date when creating an issue. Your admin must have configured the due date not to show up on the issue creation screen.

I use and develop plugins for Atlassian's bug tracker JIRA, which I find to be a good package. Out of the box it has configurable issue types, workflows, status's, priorities, issue fields, etc. It's architecture also makes it easy to develop extensions for when you need some unusual functionality. At work, we use it to track bugs, keep tabs on library loans, log time, record communication with clients, report on workloads, etc, etc. It's pretty central to our business in other words. If you're after a commercial solution, I seriously reccommend you take a look at it. As a bonus, it was built to be easily integrated with Atlassian's wiki Confluence, which has the same strengths.