Here are the combined sentences using "so, neither":

1. We won't stay here, and they won't stay here either.
2. She is studying her lesson, and I am studying mine, so neither of us is free.
3. He can’t swim, and his sister can’t swim either.
4. My son likes to drink milk, and I do too, so neither of us dislikes it.
5. She doesn’t like candy, and he doesn’t like candy either.
6. You should brush your teeth after meals, and they should brush theirs after meals too, so neither of us will forget.