First, there is an entire forum that discusses all these issues in detail. You might find that helpful. https://www.gardenweb.com/discussions/soil

Second, gardeners have differing opinions as to whether compost should be applied over bark, under bark or mixed with bark and incorporated into the soil. Your choice - no right or wrong.

Finally, it is suggested that mulch/compost not cover the crown of perennials. Otherwise, you want to avoid digging mulch or compost into the root system.

That's a good question. I really don't know the technical answer, but I'd probably rake back the mulch and put teh compost right onto the soil, unless the bark has decomposed to the extent that there's little left.

Agree with GG -- keep the compost and the mulch off the crowns.

Ditto. I would pull back the bark mulch, put the compost onto the soil, and replace the bark mulch. And yes, keep the mulch off the crowns.

:)

Dee