There's a free student plan or something for Github that you can have private repositories. Or, bitbucket.
Posting code is varies highly by teaching. I think most of my professors would have considered it outright cheating. Their interpretation of the collaboration policies was that unless it was a group assignment, you could help each other debug but you couldn't outright copy the code. Who knows who really followed that, but so long as it's in the gray area they can report you for academic misconduct. Even if it was fine for the current semester, some professors reuse homework problems. Clear it with them first.
Posting code is varies highly by teaching. I think most of my professors would have considered it outright cheating. Their interpretation of the collaboration policies was that unless it was a group assignment, you could help each other debug but you couldn't outright copy the code. Who knows who really followed that, but so long as it's in the gray area they can report you for academic misconduct. Even if it was fine for the current semester, some professors reuse homework problems. Clear it with them first.