Yes, Firefox should allow you to view secure web sites, even if they are not signed by a "trusted authority." If you get an error about an untrusted certificate, you might need to press the "Add an exception" button to tell Firefox that you trust the site anyway.

If that doesn't help, can you please provide more details about what happens when you try to use that web site?

I'll go back there and try again.

I went back to that web page and found out that it is now a trusted website.