Is this like a mother answering a phone and saying "Yes, this is Mom." or like a child answering the question "Is this your Mom?" In the second case it really should be "Yes, this is my Mom.", I'm not sure if it's technically wrong to say "Yes, this is Mom.", but as a native English speaker (American English) no one would - except a young child who would likely be told to say "my Mom" instead.
I agree, as I am english born as well. I am wondering which of these two it is.
I would say this is more likely later. I guess the reason why it is incorrectly translated into English is that it is missing word 'my' in original variant therefore it's more 1 to 1 translation rather than correct translation of the phrase.
In this case - no. This sentence conveys a message that particular person that you have been asked about is your mom. It would be valid to say 'Так, мамо' (without 'це') if you are replying to your mom.
I've never heard of the vocative case. I know Russian pretty well--is vocative a case that Russian doesn't have?
Also, Should I be able to switch the letters to Cyrillic? How do I do that? When I'm studying Russian, I learn in Cyrillic, but to tell you the truth, I forgot how I did it. I thought there was a toggle switch on the lesson page.
According to wikipedia's article on a vocative case (https://en.wikipedia.org/wiki/Vocative_case#Russian) - it used to be in ancient Russian, however it is not present in modern and can be seen only in some archaic forms. It is still used in other Slavic languages - Ukrainian, Polish, etc.
Regarding switching the letters - are you talking about keyboard layout? Normally people from Ukraine that use English on a constant basis have 2-3 keyboard layouts (English, Ukrainian and/or Russian). You can add additional layouts in your keyboard settings and chose a switching combination (Ctrl-Shift, Alt-Shift, CapsLock or any other).