Why is one -y and the other -i? And how do I know if the neuter/feminine ending is -ie/-ia or just -e/-a?
Non-native speaker here. I'm afraid that you cannot know which are -i adjectives for sure. You can only memorize them (except when it goes after g/k: almost always i)
But if you know the base form is soft (-ni), then all its other forms are soft (-nia, -nie, -nich)
Not necessarily. They are the next and the previous day only with respect to today.
Tomorrow, yesterday is a reasonable translation evebn if polish also has specific words for this.
"Will you return the same day as your sister?" "I also might return the previous day or the next day."
It depends on your point of reference. If you are talking about today, the previous day would be yesterday, and the next day would be tomorrow.
Now imagine you're telling a story about a specific day in the past, your birthday last year, for example. You might want to talk about what happened the day before your birthday, the previous day, or what happened the day after your birthday, the following day. In this case you could not use the words "yesterday" or "tomorrow".