In our neck of the woods, you're more likely to find composted/aged pine bark. And it's an excellent growing media. One of the best I've ever used, in fact.
That's exactly right. Phosphate takes time to break down in soil. And there's more biomass, hence more microbial colonization, and more biodiversity. You will literally not in a thousand years get rock phosphate to break down in a container, short of making the media so acidic, that it won't grow a plant.
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Mushroom compost is composted horse manure. (along with bedding) It's too heavy to use straight, because you get too much rain. If you lived in a desert, I'd say go for it.
Calcium is totally unnecessary for soil anywhere on the East Coast. For containers, different story. What is your current pH?
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Calcium nitrate is not readily available. Useless. You'll have better results with Epsom or calcium acetate. (vinegar and eggshells)
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BER is commonly caused by heavy rain, and disruption of nutrient uptake. But I can't say that authoritatively, without knowing your story. What have you fed it so far? (for calcium supplementation) Containers, right?