Are all fungi producers?

No. Fungi are decomposers.  A producer, makes its own food. A fungus does not make its own food, it breaks down nutrients from dead organisms to get a part of what it needs to survive. Which is why it is called a decomposer.

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a. to encourage apoptosis

the solute can move "downhill," from regions of higher to lower concentration, relying on the specificity of the protein carrier to pass through the membrane. this process is called passive transport or facilitated diffusion, and does not require energy.