'How do the daffs and tulips grow past the bulbs above them??'

Not sure if I properly understand your concerns about this. Simply put, the shoots of the lower bulbs push the others aside (think of how plant shoots can emerge through concrete), though the shoots are of course also more streamlined than in their above-ground form.

'if I add 2 inches of mulch on the top of the bed I am planting the bulbs, is it recommended that I subtract that depth from the depth I plant the bulbs?'

Planting depths are only a guide, and a pretty rough guide at that. Obviously the actual depth a bulb feels 'comfortable' with will vary with the conditions it finds itself in. An extra couple of inches won't make much difference. If, when you later dig them up, the bulbs are at a different depth from where you left them you'll know what depth to aim for in future plantings.

I have daffodils that return and are planted at their happy depth of about 6 - 8 inches here. It varied because I have a line of red clay whose depth varies and I really don't want to put them right in the heavy stuff.

On top of that I plant crocus, tulips, Dutch Iris anemones and cool annuals like pansies. The daffs seem to come up and fill the area no matter who is on top.

I've "layered" bulbs, and it works. Don't know why, but the flowers don't seem to mind, and it sure helps when you don't have lots of space.

I put dutch hyacinth on bottom (they're the largest I had), cover all but the tip; put tulips above them - again cover all but the tips; but crocus, squill, etc. on top of them, and completely cover all. And if adding 2" of mulch, put the bulb that needs 6"-8" at 6", and it'll be just 8" when finished.

Yes, layering is fun. You can fit a lot of bulbs in one spot. I like to put lilies way down deep then plant other bulbs on top as bulbs explained. It's the best way to extend your bulb season well into summer.

I find Allium the best bridge between spring and summer. :-)

What happens when the blooms go away and only the foliage remains? Does the next bulb just push through it? And then do you leave all the foliage until it turns brown? I'm trying to imagine how this works with 3-4 layers of bulbs...

Foliage has no problem pushing through. I leave all my bulb foliage alone until it turns brown.

Sunset Magazine did a great article on layering bulbs a couple of years back. It may still be available online.