The only valid statement here is #2. The reason for that is that the people don't elect the president, the states do. The individual states are free to decide how those votes are distributed, either proportional split or winner take all.
Without the EC, smaller states wouldn't have any say in the presidential election. So while the EC may be unfair on a personal level, it's fair on a state level.
The same is true of the senate, each state gets two, no matter the population, isn't that unfair? Why should California and Montana have the same number of senators? Shouldn't those be proportional like the house?