If we remove DataSource rows from a DataSource, would that mess up any previous Forms? Or does it cause any problems with pulling data from those old forms through the API?

If you remove DataSource rows from a DataSource, any previously completed Forms will not be affected.

But, anyone who attempts to use the corresponding database field that references the removed DataSource rows would be unable to select the rows you remove. This could cause issues for your Form Users.

To maintain the integrity of your database field, validate that your Form User will not need to use the corresponding database field when filling out a Form.