Does saving a draft generate the report immediately?
No. Saving a draft only stores your field and section selections. You still generate the report separately using that saved configuration.
Are Search Progress Report drafts and Search Summary Report drafts the same thing?
No. The two report types have different fields and sections, so drafts for each are saved and managed separately.
If I change my default report settings, does that update my saved drafts?
No. Each draft keeps the configuration it was saved with, independent of your default settings.