I got this question when I was doing my English test paper where the writing section is to give advice on whether students should study abroad or study at home, clearly, at first sight I can tell "study at home" here certainly doesn't mean "study in one's living place" but as opposed to "study abroad" and I have no difficulty understanding it, the web search I did also proved "at home" does have the meaning of "in one's own country", but the thing is what if the phrase is used in isolation without the contrast given by abroad, like "I want to study at home in the future" or maybe "I wanna run a grocery store at home" would it still be proper that I just say so to mean these activities are to take place in my country but not my literal house? Will people still see what I mean? I also wish to know some other related idiomatic expressions that fit the case. Thanks for your answers.
at home is only used about your country of origin if you are not in it at the moment. For example:
I like the food here, but it's not the same as at home
It could be used by somebody who is currently abroad to describe their own education plans or those of somebody from their own country.
I am planning to go home to study Economics
Jason went home to finish his PhD.
If you were in your own country, I would assume that any reference to education at home would mean study at your place of residence.