"I have a red umbrella."
Translation:Ich habe einen roten Regenschirm.
It also accepts the general term Schirm as a common abbreviation of sorts that would be understood through context.
Not really. "der Schirm" is the main word for such canvases with such a form. There is also "der Sonnenschirm" = "sunshade" and "die Schirmmütze" = "cappy" and "der Fallschirm" = "parashute" and "der Lampenschirm" = "lamp shade" and "Windschirm" (against wind), "Blendschirm" (shade in a car) and some more. So "Regenschirm" is just the thing for rain.
Sure, but my understanding is that I could say Schirm in situations where the context makes it clear what kind of -schirm it is, and that saying Ich habe einen roten Schirm would, without any further context, be interpreted as meaning an umbrella (rather than, say, a shield or other type of -schirm). Is this not correct?
It's like saying "coat" instead of "raincoat". It is not an abbreviation but another word. And you are right, context can help to fill in the information that the less specific word omits. I just wanted to avoid that people think that "Schirm" instead of "Regenschirm" is like "'cause" instead of "because" or "jet" instead of "jet aircraft".