At the ends of the mitotic spindle are the centrosomes, the areas where the microtubules come together and are organized. You may see a cross there which representes the centrioles, a main part of the centrosome. B, then, is the mitotic spindle which is made up of microtubules. Now, in the chromosome the point where the DNA is highly condensed and allows the sister chromatids to attach to each other is the centromere. On the outskirts of the centromere are the kinetochores which allow the microtubules to attach and eventually pull the chromosomes apart (think of movement, kinetics.) Finally, as this is the metaphase stage, the dotted line represents the metaphase plate where the chromosomes line up. There is no dotted line in reality, it just helps to use one to understand the concept.

The vocabulary can be a little bit confusing since there are similar terms. Chromosomes, when not duplicated, are thread-like and can appear to be a single unit, A. But when a chromosome is duplicated then that is when you get the "X" shape. Each copy of the duplicated chromosome is called a chromatid and since the two copies are identical that is why they are called sister chromatids. Now, since an organism gets one copy (allele) of the same chromosome from each of their parents that means that during mitosis the duplicated chromosomes are of both the mother and father which join and form a tetrad. Note that you cannot have chromosome 1 and chromosome 3 join together; they have to be homologous, or of the same function/type which is how the tetrad is known as the pair of homologous chromosomes. Finally, to promote genetic diversity, crossing-over occurs in the tetrad and the tips of the chromosomes interlink and switch places at the chiasma so that when separated the daughter cells aren't solely of the mother genes or father genes but of both.

The ribosomes are responsible for the assembly of proteins. These structures link amino acids together to form a polypeptide chain which gets folded into a functional protein. Note that ribosomes are not membrane-bound organelles.

Microtubules make up the spindle apparatus and is responsible for the separation of homologous chromosomes in cell division. Microfilaments make up of actin which is responsible for muscle contraction. Ribosomes help make repairs in the cell and aid in protein synthesis. Nucleus stores DNA and the mitochondria produces ATP. Although all of these play a role in cell division, without microtubules cell division will not occur.  

The mitochondria is often referred to as the powerhouse of the cell because it is the location of cellular respiration cycles (Krebs cycle and electron transport chain). Thus, mitochondria is responsible for providing most of the energy for the cell in the form of ATP.

The Golgi apparatus is located within the cell cytoplasm, not the cell membrane. All other options are true characteristics of the cell membrane.

The mitochondrion is known as the powerhouse of the cell, because it creates so much of the energy needed for cellular processes. ATP is another source of energy. The mitochondrion would be responsible for producing the mitochondrion. The other structures are responsible for other processes, like storing DNA or photosynthesis.

Microtubules are involved in providing motility, because they are essentially conveyer belts that move things like vesicles, granules, and organelles like mitochondria via special attachment proteins. They are a component of the cytoskeleton. They are composed of the protein known as tubulin, are made of centrioles, and they develop from the plasma membrane.

This is because ribosomes assemble amino acids into proteins. Such activity would be found associated with rough endoplasmic reticulum and not the smooth ER. The smooth ER is majorly responsible for breaking down toxins and manufacturing things such as lipids and hormones.

Lysosomes are largely involved in breaking things down, because they contain acid hydrolase enzymes that break down waste materials and cellular debris. They can be described as the stomach of the cell. Lysosomes do not produce these other things. Things like ribosomes, Golgi apparatus, and the mitochondria are involved in these other processes.