"My grandmother lives in that village."
Why do you have to put watashi no before sobo? Sobo is your own grandmother, right?
I reported it. You don't need 「私」for the personal versions of relatives' names. The fact that you're using those versions makes it clear you're talking about your own grandmother.
You're not wrong, per se. Here is an example where your answer works:
You've used が because you were answering my question. In Duolingo's answer, they've used は because they are starting the conversation, rather than answering my question.
I got a different correction for the same sentence: そのむらにはわたしのそぼがすんでいます。 I'm not sure about what difference the は makes in this case.
It is a difference in focus of the sentence. Your sentence translates as roughly, "That village is where my grandmother lives"
この means "this." The word you are looking for is その for "that." そのむらには私のそぼがすんでいます is accepted. Presumably そのむらには、would be accepted as well, though I don't think the 、 is needed.