When I log in through my Nokia Classic device, a delete button appears at the bottom of my answers. But when I click the delete button, the page simply reloads instead of deleting my answer. Is this a bug?
Well, it appears that classic Nokia comes with Nokia Browser for Symbian as the default browser.
Stack Exchange sites are not supporting all existing browsers. List of supported (and explicitly unsupported) browsers can be found here: Which browsers are officially supported, and what else do I need?
Try installing standard mobile browser like Chrome or Firefox and everything should work fine.