What you are going through is entirely normal. Given your time frame, it sounds like you're right in the middle of what's called the "trough of disillusionment", which is a typical stage in the process of culture shock. I'm going to take a guess: When you first got into the country you were having a lot fun. All the differences of the new culture were exciting and you really enjoyed exploring your new surroundings. But then over time it started getting annoying. You started missing the comforts of home and the strangeness of your new location really started to set in. This was compounded by the fact your job started getting hard when your old boss left and now you just want out, you're done.
Most people go through a cycle like this when they immerse themselves in a new culture. At first everything is fun and exciting, but over time it wears down and can get downright depressing. This is very common. But if they stick with it and fight through that trough, what they find is things tend to get better. Eventually their new surroundings start becoming more familiar and eventually they feel just like they're at home.
So before you make any decisions, ask yourself if you really want to go home now, or if you are just in middle of the low point of this very common cycle. Do you know anyone else from your home country? Go out to get a coffee with them. Call a friend at home. Try and find some little comfort that reminds you of home. Maybe a restaurant that serves food fro your home country. Take some time for yourself and remind yourself that things will get better. It would be a shame to give up on a cool experience like this just because of a temporary bad feeling.
Unless you have a contract locking you in place, you really don't need a reason to resign. Employment is generally a free will thing. You can leave for any reason or no reason. So, if you decide you really do need to go home. That it is all just too much to take, I think saying you miss home and want to go back is a perfectly valid reason to resign. But I would ask you to consider whether that is something you really want to do first.