All the answers are correct and show reactions that are necessary in the process of cholesterol synthesis.Cells receive cholesterol from dietary lipoproteins such as low-density lipoproteins and high-density lipoproteins. However, cholesterol can be synthesized " de novo" by the liver directly from acetyl CoA thru a series of reactions described above. HMG-CoA reductase, the rate-limiting enzyme in the process is stimulated by insulin and inhibited by stain drugs.

Triglycerides are produced in the adipose tissue and liver. Their production is regulated by insulin and glucagon. They are not directly regulated by growth factors or antidiuretic hormone (ADH). Also, they are transported in the blood as lipoproteins, but are not produced in the blood.

Fatty acid synthesis occurs via the addition of acetyl-CoA carbons to a growing fatty acid chain. And so, in order to create fatty acids from glucose, there must be a link between the two molecules. That connection is the acetyl-CoA that is formed from pyruvate at the end of glycolysis and the pyruvate dehydrogenase complex. However, fatty acids can not create pyruvate, as there are no enzymes capable of this reverse reaction.

Acetyl-CoA carboxylase is high in adipose tissue, lactating mammary glands and liver where fatty acid synthesis is important. It has two catalytic activities as a biotin carboxylase and carboxytransferase. Acetyl-CoA carboxylase converts acetyl-CoA to malonyl-CoA. Compared to other enzymes that are phosphorylated when active, acetyl-CoA carboxylase needs to be dephosphorylated in order to be active.

The two carbons that remain after the addition of malonyl-CoA are added as an acetyl group with the carbonyl carbon on the interior of the chain, which is to say a ketone. Then, the carbonyl is reduced to form an alcohol. Next, the alcohol is dehydrated to form an alkene. Finally, the alkene is reduced to saturate the chain, forming an alkyl group.

Carnitine transports fatty acids from the cytosol to the mitochondria. Acetyl-CoA is converted to citrate as it exits the mitochondria and enters the cytosol.

In fatty acid synthesis, all of the enzymes listed are are regulated by insulin. Pyruvate dehydrogenase transforms pyruvate into acetyl-CoA. Glucokinase transforms glucose in glucose 6-phosphate. Acetyl-CoA carboxylase converts acetyl-CoA to malonyl-CoA. Fatty acid synthase converts malonyl-CoA to fatty acid palmitate. Insulin regulation is essential for proper utilization of dietary carbohydrates and lipids after meals. 

The citrate shuttle moves acetyl-coenzyme A (CoA) from the mitochondria to the cytosol to make it available for fatty acid synthesis. The process involves multiple reactions and enzymes such as citrate lyase. Citrate acts as as a carrier agent for acetyl-CoA molecules from the mitochondria to the cytoplasm and in reverse. Oxaloacetate, a product of citrate lysis in the cytoplasm is not moved directly back in the mitochondria, but rather is converted back to malate and pyruvate.

Acetyl-CoA carboxylase is essential for fatty acid synthesis, it provides malonyl-CoA, necessary for production of palmitate, a fatty acid. The enzyme is regulated via phosphorylation and dephosphorylation. Insulin activates the enzyme by dephosphorylation. Glucagon and epinephrine deactivate on the other hand the enzyme by phosphorylation (adding a phosphate group to the molecule). Citrate activates the enzyme while palmitoyl-CoA, the end product of fatty acid synthesis, inhibits it.