Need technical advice concerning web proxies

Currently doing a research on using web proxies as a means to bypass Internet censorship, using my ISP as a research platform, this is a term paper, studying for my M.Sc in Computer Science.

Now, I noticed that when I put in a proxy from an online proxy list(#-Link-Snipped-#) in the proxy settings of my web browser, say Mozilla Firefox, I also put in port as 80. I then set the homepage of my browser to the homepage of my ISP (www.[i]isphomepage[/i].com). When I click homepage, my ISP's homepage loads up immediately. But to surf outside sites like yahoo.com is impossible. Any way to do that? Also when I use 209.85.129.99(Google IP) as my proxy and port as 80. When I click homepage, Google search engine loads up. I observed however from the page loading bar that it shows (loading from www.[i]isphomepage[/i].com), however, <a href="https://www.google.com" target="_blank" rel="nofollow noopener noreferrer">Google</a> shows up in the address bar up above. Now when I put #-Link-Snipped-#, Google news comes up. When I try to navigate to other newspages or try other sites like <a href="https://www.yahoo.com" target="_blank" rel="nofollow noopener noreferrer">Yahoo Search - Web Search</a>, it doesn't work. Can anyone tell me how to navigate to other sites if possible. For the record, my normal ISP connection uses no proxy settings. Thanks.