Yes you certainly can, and can also have a bunch of other ERC20 tokens (for ETH acc) in there too. Its not just ETH, and ETC. There are about 20 others, as well you can custom add tokens so many more will be added in the coming future I am sure.
seems you can. If you click on the top right you can switch it to you can switch to ETC etcpool.io. I clicked it and magically found around 300 etc just sitting in my wallet so pretty lucky for me
seriously? wow somebody just handed you a bundle of $$. Good for you, sucks to be them. Always double check your address folks.