Yes. To remove a sender address do the following:
Not at all. Because of the spam laws in various places, sending commercial messages anonymously is highly frowned upon and even illegal in some places. So we do our best to make sure our clients are safe from litigation. Besides, it's the best practice to let your customers see who they're talking to anyway.
Well, it really depends on the situation, but employees leaving will change your email addresses, and therefore you'd have to change it then. As well, if the account changes hands or your email is compromised, you will want to change your sender address to avoid any issues there. Any number of factors could influence the change, the important part is you're always able to when you need to.