1. Why is c<->c&d = c→d? A biimplication is a conjunction of two implications: (c → c&d) & (c&d → c). The right implication is just a tautology. The left implication c→c&d can be simplified to c→d. Do you see why?
2. Why is c & ¬d | ¬d = ¬d? Let's look at all possible assignments. For the not-satisfying assignments, it's trivial. They neither satisfy c&¬d nor ¬d. Removing one of them doesn't make a non-satisfying assignment satisfying. What about the satisfying assignments? The satisfying assignment could satisfy ¬d. Or it could satisfy c&¬d. If it does so, it also satisfies ¬d. Hence, all satisfying assignment satisfy ¬d, and adding or removing (c&¬d) doesn't change the satisfying assignments.