If you feed plants with compost, it will do well. Better than it would without it. (Unless it's a cacti maybe.)
You feed the soil organic matter and let the plants take what they need. To do this, you build humus in the soil. That fine broken down layer that occurs between mulch and soil. That's the good stuff. If you build healthy rich deep soil, you've fed your plants. Then all they need is water.
So mulch, minimise chemical use, encourage earthworm activity, and add compost and more mulch. Lucerne/alfalfa, green manure crops, animal manures, fish and seaweed extracts etc. These things all feed the soil organically, slowly releasing their nutrient at a rate that somehow just happens to be the right rate for your plants.

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The secret is the soil.

Depends on the plants and the degree to which the bark has aged Danno. I'd use weathered bark on citrus for example, or a perrenial garden bed, but not on vegies as it takes too long to decompose.
With the grass clippings, they can carry grass seed, so you may be adding weeds, and they can also mat down and prevent moisture penetration, but mixing them with leaves helps prevent this. Re the nitrogen drawdown, that is a problem with green materials breaking down, using up the nitrogen in order to begin decomposition. Once aged a little though, these mulches are fine. A handful of pelletised chicken manure will supply nitrogen to this process anyway.
I use my clippings in the compost bins, straw/hay for vegies etc and shredded trees and branches for perrenials and fruit trees.

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The secret is the soil.