Do I need to have a proxy server to have HTTP over SSH

It may be that the proxy is only allowing access to HTTP/HTTPS ports (80 or 443). I've worked around that by changing the SSH server to listed on port 443. That made the proxy I had to go through allow the connection, but if you can't change the SSH server then you may be out of luck.

Your SSH command with -D is fine (so the SOCKS will tunnel it's just the connecting to the SOCKS via HTTP, that you have to sort out)

I get good output with

curl --socks5 127.0.0.1:8080 http://blah

but I get the same wrong output you get if I do

 curl --proxy 127.0.0.1:8080 http://blah

So, firefox is connecting as if it's an HTTP Proxy

Looking at the firefox window

manual config YES

you said you ticked "use this proxy server for all protocols" That is a totally wrong move! You want to enter a SOCKS proxy, and if you do that then the SOCKS box get nulled/greyed out and you can only enter an HTTP Proxy.

So don't tick that.

And do, enter the socks proxy ip.

and remove where it says no proxy for 127.0.0.1,localhost . if it says that, which is default.