For the connection, it has more to do with your distro than it does with KDE.
As for Firefox... I used KDE 3.5.1, 3.5.6 and 3.5.7, and never had problems with it as default browser. What you can try doing though, is right clicking an HTML file, Open With... > Other... > Pick Firefox from the list of apps or type 'firefox', and tick 'Remember association application for this type of file'.
If you still have problems, you can try doing the association manually:
Open the Personal Settings module (K Menu/Kickoff - search for "Personal Settings", "Configure Desktop" or simply search for/run "kcontrol"), go to KDE Components > File Associations, search for "html", open the "text" tree and click "html". On the right you should be able to control what apps can handle HTML files, just make sure you have Firefox there and it's on the top.