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Email is the only method of communication we have to get in touch with you. It is very important that you keep your email address updated and accurate with us at all times.
Yes, but be sure that you are checking that e-mail account often. If someone accuses you of an unreported match or we need to get in touch with you, the e-mail will be sent to that address. There have also been quite a few incidents of free mail accounts being hacked lately. The number one mistake people make is to make their "password hint" too easy or a question that the answer to it IS that user's password. The bottom line is to be very careful when using free email services, but that they are allowed.
Contact your Admin Team, and explain that you have not received your activation key and they will help you activate your account. Sometime the reason you don't receive your activation key is because you entered your e-mail address incorrectly when you signed up, so verify that you entered the correct e-mail and include it in your mail to them.
Yes, on most Leagues. The decision rests with the Head Admin of the League whether or not to require this. However, even if it's not required, it can be useful to at least have a similar name, so that people don't get confused as to who you are.
You should create your account on the gaming service first, since name choices are so limited there. Once you have an account at the gaming site, you can edit your username on the League by going to the "MyAccount" tab and clicking on the "Edit Username" link listed under "My Options". Alternately, you can try to make your gaming site username as similar to your League username, provided that this does not break the rules of your League.