I am testing a program that is a terminal emulator that runs through a web browser. I'd like to use a free UNIX shell service to test the function key maps (this program can also generate a function key map or you can manually put one in). I ask this because someone wants to be able to use the arrow keys and things of that nature.
I think you will struggle to find a service that gives you gratis access to a terminal on any server on the Internet unless you have friends that host these kinds of services.
You can try to use virtual hosts for your problem, meaning that you install a hypervisor on your machine, then install the operating system you want using that hypervisor and test your software that way.
There are several hypervisors that can be used and that are as far as I know gratis to use.