<ol>
<li><p>Is there a open source or free suite that can integrate testcases, tests, bugs and possibly the fixes(source code) together. Maintaining the requirements in this system is not a necessity (though, it would be nice to enter a requirement id for each testcase in a custom field). We are a small organization and cannot afford something like HP Quality Center.</p></li>
<li><p>We have coding skills (Java, SQL), so if it comes to integration of different tools using Java APIs, it should not be a problem. Similarly, a practical solution using export/import of results/data should also be fine (we could automate where possible). </p></li>
<li><p>Has anybody used PushToTest TestMaker as part of such a solution.</p></li>
</ol>

This link
http://www.testingfaqs.org/t-management.html
has a list of test case management tools, both freeware and commercial. Maybe there is something on that list which can meet your needs.
Another posibility is something like
Trac
. That is not really designed as a test case management tool but it integrates a Subversion repository browser, a bug tracker and a Wiki. If you can manage organising the test cases on the Wiki then that will let you link the Wiki pages to bugs and bugs to Subversion commits. We used to use Trac and were quite happy with it. We switched to Jira because we wanted some more bug tracking features.
I have not used it, but Trac does have a testcase management
plugin
listed on their web page.