Regarding the process of exporting proteins, does mRNA leave the nuclear pore and head towards a ribosome within the ER or a free ribosome before getting packaged and exported via exocytosis out of the cell? And if it does go to the rough ER, what does the ER do other than make it into a protein? Does it just offer a nice smooth route to the golgi?
Okay the important thing is the destination of the protein. If the protein will carry out its function within the cell, the protein is synthesised at the free ribosomes. However, if the protein (e.g. insulin hormone) needs to be exported out of the cell, it is synthesised on the ribosomes attached to the rough endoplasmic recticulum. Take that as a rule - remember, the rough endoplasmic reticulum partially modifies the protein, but mainly just transports it within the cell to the Golgi complex, where the protein is modified further, and packaged into secretory vesicles that bud off the golgi body, and leave the cell by exocytosis.
For protein structures, I'm struggling over the difference of quartenary and tertiary structures. My teacher and peers keep telling me the difference is in the 3D shape, but aren't both of them 3D in terms of having secondary structures held together by various bonds?
The quaternary structure of a protein refers to a protein being made up of two or more polypeptide chains. The quaternary structure just refers to the overall 3D shape of the protein as a result of bonds forming between the side chains of the polypeptide (i.e. bonds forming between the R-variable groups of the amino acids). But you're right, both the tertiary and quaternary are 3D shapes of a protein. Not all proteins need to have a quaternary structure, but ALL proteins must have a tertiary structure. Remember, the tertiary structure of a protein is critical to its function (e.g. the tertiary shape of an enzyme's active site is specifically complementary to one specific type of substrate that the enzyme acts on).
What cells other than macrophages and Natural killer cells have class II MHC markers? And are they used to present antigens of a pathogen so that specifically, t helper cells can activate an immune response? What other cells use MHC II markers for attack? Do Tc cells recognise the antigens and kill cells with that antigen on their membranes, or do they just check the MHC I markers for self membranes and attack if there isn't?
Macrophages, B-lymphocytes and T-lymphocytes possess Class II MHC markers. For example; a macrophage binds to, engulfs and destroys a pathogen; once the pathogen's antigens have been fragmented (and epitopes produced), the MHC class II markers of the macrophage grab these epitopes and migrate to the membrane of the macrophage. They are then known as an antigen-presenting cell. Why? Funnily enough, they present the antigens. Once a macrophage docks with a helper-T cell, helper-T cells release interleukin-2 (you don't need to know this), and a humoral response (mediated by B-cells, antibodies) and a cell-mediated response (mediated by cytotoxic t cells) is activated.
When a cell (just a nucleated cell) becomes infected (e.g. epithelial cells of the small intestine), epitopes (antigen fragments) are grabbed by MHC Class I markers, which again migrate to the outer surface of the cell, signalling cytotoxic t-cells. When a specific cytotoxic t-cell recognises the specific antigen presented on the MHC Class I marker, it docks with the cell, releasing perforin. Perforin is a protein released, which punches holes through the plasma membrane, lysing the cell and eventually destroying it.
Hope this helped!

And Irving4Prez is also right; thought a second input may be helpful haha