Penguins have a long list of predators:
Sharks
Many Types of Seals
Killer Whales
Another way that penguins are dying is rapid melting of the ice in antarctica due to global warming, it is said that they could be fully extinct by as soon as 2100. Lastly, penguins are very prone to catching diseases such as Salmonella, E. coli, West Nile virus and Avian pox virus infection.
Emperor Penguins don't have very much competition but one of the times that they do is when they are finding their mates, when they are finding their mates they perform dances and other special rituals that they have to try to get the mates that they want. Another time that they compete is when they are fishing. This competition however is with other animals and not with their peers like the breeding is.
Invasive species don't directly affect the penguins, however they do affect the habitat that the penguins inhabit by making them uninhabitable.
The Emperor penguins IUCN rating is Near Threatened which means that they are pretty safe for the foreseeable future. The penguin population is at 560,000 penguins or 280,000 breeding pairs. The population is on a negative trend as you can see on the graph they are expected to go down even more.
Humans have impacted Emperor Penguins very heavily by emitting Co2 into the game and causing global warming that melts the ice in antarctica which is the habitat for the Emperor Penguins. Humans haven't impacted penguins until more recently if you look at the history of humankind. It all started when humans found the birds and actually started hunting them for food. Now, humans are trying to limit global warming for many reason but melting of the polar ice cap is definitely one of the big reasons. People are trying ot limit emissions on factories, cars, etc. that cause global warming.