With your schedule, it is going to be difficult to housetrain such a young puppy to go outside. Because she is such a small dog, how about papertraining her? You could provide her with a little box that she would use to do her business in. This is sometimes preferable for small dogs due to weather conditions. At least here where I am, the winters can be quite brutal for such small dogs, some refusing to go out when it is snowing or when it is really cold, even with a coat on!
Would it be possible to have your neighbour come by every day during the day and on the nights that you go to your classes? Your hours are such that she would be home way too long and wouldn't be able to hold for that long. There would definitely be accidents.
Because of her breed, I would be hesitant to only feed her in the morning and night. Many times small dogs need to be fed 3 times, especially puppies. The water should always be available to them.
I think that it may be unfair to her to ask her to wait for your return to go out to do her business. A litter box would be much better with your schedule. It is possible to train her, it just may take longer because you are not there to correct her when she does something wrong and to praise her when she does the right thing.