A "visual approach" is an instrument flight rules operation. The flight was still IFR and had requested/been cleared for a visual approach, but had not switched to VFR (which they'd do by cancelling IFR).

When they accepted the visual approach, they took responsibility for navigation and terrain/obstacle clearance.

Yes... though I'd include the subsequent quote "and responded that they would cancel IFR “in just a couple of minutes.”"

Also someone is correctly pointing out to me downthread that a visual approach is technically an IFR procedure under IFR not VFR flight rules (the latter basically meaning you aren't using instruments at all). I'm assuming IFR in the summary is referring to the non-visual approach (rnav or ILS) but the preliminary report is I suppose ambiguous as to that.