I don't whirlpool with a pump, but my understanding is that you shouldn't need hop bags/hop spider if you whirlpool (especially with a pump). When I add late additions I usually do a hot stand for 15-30 minutes after flameout if I'm looking to get IBUs from those late additions (if I'm mostly looking for aroma I chill immediately).
I use hop bags and I don't remove the hops until after I've chilled the wort. I whirlpool with a spoon and let the kettle sit undisturbed for around 20 minutes to allow the trub to settle in the cooled wort (with the lid on and chiller removed). I honestly don't think I benefit much from whirlpooling with a spoon which is why I still use hop bags, but the cold break and other trub settles nicely from the cold stand (mostly thanks to whirlfloc I assume). I typically leave a gallon of wort behind - with BIAB I seem to get a lot of trub.