What carries over from a Chapter 1 save file into Chapter 2?
Solution 1:
As Kevin mentioned, your money and inventory carry over from Chapter 1. Your save file name also carries over. If you defeated Jevil, you will have a Shadow Crystal in your inventory. (The crystal can be imported later after starting Chapter 2).
Below is an incomplete list of changes based on actions in Chapter 1:
- If you spoke to Noelle after returning from the dark world, Noelle can give Susie a lunchbox with chalk as a gift when inviting her to study at the library.
- If you spoke with the original Starwalker, they will join your party as a key item and appear periodically throughout the chapter (Thanks LeonardPlayz).
- The customized "machine to thrash your own ass" built in Chapter 1 will reappear in the boss fights against Rouxls Kaard and The Queen.
- If you have the Devilsknife or Jevilstail from Jevil equipped when encountering Tasque Manager, she will comment that she hates chaos (Thanks HyperBeast43).
- If you met with Onionsan at the park, you can meet Onionsan again on day 2. Otherwise, an NPC will tell you that you could have met someone if you were there yesterday. Standing by the water for a few seconds will cause Kris and Susie to sit down together.
Solution 2:
The most significant change is that your inventory and money will carry over, including the ability to get replacement Spin Cakes from Top Chef if you gave him the repaired Top Cake in Chapter 1. In practice, this means an imported save will usually go into Chapter 2 with a large volume of healing items, unless you used them all up fighting Jevil or something. There are a number of other, smaller changes, but in most cases, they aren't really that important (e.g. minor changes to dialog). The only major exception I'm aware of is Jevil, whose defeat carries over and is implied to carry significance to the plot (if you talk to Seam in Chapter 2, anyway).
As of version 1.07, if you defeated any enemies with violence in Chapter 1, this is acknowledged in Chapter 2, but has no real effect. If you do not import a save, it's assumed that you played pacifistically.