Problem : Will you find the same set of membrane proteins in each cell membrane?

No. Membrane proteins perform a number of functions within cells, as a result, different proteins are necessary in different regions of cells depending on the function of the cell and the interactions it may take part in.

Problem : What are the names of the two main classes of membrane proteins and how could you tell one from the other?

The two main classes of membrane proteins are integral versus peripheral proteins. Since peripheral proteins are easily dissociated from the lipid bilayer, one could treat a cell with a mild detergent that does not disrupt the cell membrane and then see if the specific protein remains associated with the lipid bilayer or is removed.

Problem : What is the name of the configuration that membrane proteins adopt in regions that span the lipid bilayer?

This configuration is called an alpha-helix. It is the same structure that DNA adopts naturally.

Problem : Which class of proteins, integral or peripheral, are freer to move around within the lipid bilayer?

Integral proteins can be thought of as icebergs that float in a lipid bilayer sea. They are relatively mobile in the cell membrane.

Problem : The cell surface is covered with an additional set of molecules. What name is given to these structures and what is their function in the cell?

The cell surface is covered with a cell coat or glycocalyx which consists of carbohydrate chains. They help protect the cell from damage.