Recently my saved print Tomdispatch articles were being saved as" Dillo" articles which
got on my nerves as I never use the Dillo web browser. I went into synaptic and removed it.

Later nothing worked on my AntiX12 distro; not even a new installion containing my old
files. so I had to spend two days re-installing a fresh Antix12 distro.

Is removing the Dillo browser supposed to shut down the operating system or was there
some malware in my computer that caused this to happen??

I have noticed that the Dillo web browser, is a part of Antix. When you open any help links on your menu. It uses Dillo. As part of the system I can't answer that one.
When it comes to malware it is usally short lived within linux, It may cause a hipcup in a browser. But I have never seen malware that will bring down the Linux Operating System.