The molecule which is repeatedly added to a growing fatty acid is malonyl-CoA. Malonyl-CoA is synthesized from acetyl-CoA (two carbons) and  (one carbon), and, thus, contains three carbons. Of course, it is important to remember that the  of malonyl-CoA leaves during the reaction with the acyl chain being synthesized. 

Adipocytes stock mainly fatty acids, not glycerol; glycerol produced during triacylglycerol degradation is shuttled through the blood to the liver. Lipase does not digest chylomicrons, but rather triacylglycerol, producing glycerol and fatty acids. The lipids (fatty acids) in fatty tissue mostly originate in our diet, not in our liver. Mammals specifically require certain polyunsaturated fatty acids which they are unable to synthesize, like linoleate; these are known as the essential fatty acids. Chylomicrons are proteins which carry triacylglycerols, cholesterol, and other lipids, obtained by the diet, away from the intestine. Chylomicrons are created in the endoplasmic reticulum of small intestine cells i.e., enterocytes and exoctyosed into lymphatic capillaries.

The proper order for fatty acid synthesis is condensation, reduction, dehydration, and reduction once again.  This creates an activated acyl group that has been lengthened by two carbons through this anabolic biosynthetic pathway.

The sources of glycerol-3 phosphate for triglyceride synthesis are glycerol in the liver, but not the adipose tissue (adipose tissue does not have glycerol kinase) and from the conversion of dihydroxyacetone phosphate (obtained in glycolysis) to glycerol-3 phosphatase in liver and adipose tissue. Triglycerides are one of the most important forms of storage of lipids in the body. 

Triglycerides are the major form of storing dietary lipids in the body.Triglycerides are composed of three fatty acids and a glycerol molecule. In glycerophospholipids the third fatty acid of a triglyceride particle is replaced by a phosphate group and a choline or inositol group. Choline groups are ammonium salt groups in neurotransmitters or phospholipids on cell membranes. Inositol groups are found in second messengers. Glycerophospholipids are part of the cellular membrane and are sources of second messengers such as diacylglycerol and inositol-3-phosphate. 

Cholesterol ester transfer protein's role in lipid metabolism involves transferring cholesterol esters or triglycerides between different types of lipoproteins in the blood. It is not part of the lipoprotein particle and is not a receptor but, rather, a protein in the blood. Cholesterol and triglycerides are carried in the blood by lipoproteins, which depending on the amount of protein contained are: chylomicrons, very low density proteins, low-density proteins, intermediate density lipoproteins and high density lipoproteins. 

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.