Accessing SharePoint 2010 through browsers other than IE

Hi there,

I'm new to SharePoint server management, so please bear with me. As part of a project to introduce SharePoint 2010 to the network at our School, one of the requirements is to be able to access SharePoint from the Internet over HTTPS. We've purchased a certificate from a trusted CA, and extended the web application to port 443. We're having a couple of issues now;

We're able to access the site from the internet now, with a auth prompt, but we can only login through IE. Any other browser asks for authentication repeatedly, it won't show an error, it just keeps re-prompting. Before the application was extended to 443, we could login through Chrome, Firefox and Safari, but now all three experience the same problem.

Documents opened from the site in Office always open in Read-Only mode (only exception seems to be Publisher documents). If we try and save it to the SharePoint site, we can browse all the directories without a problem, but when we click Save, we get an error saying 'Upload Failed'. Permissions are not the problem, as the Owners group also experience this issue. Once again this also appears to be happening since we started using secured http.

Any help would be greatly appreciated. Many thanks!