i've never shipped from microcenter (since i just visit the store) but most likely they use ups or fedex in which case standard shipping is normally 5-7 days. as far as calling you, who do you want to call and why? typically tracking orders are sent out via email from most companies so i would expect microcenter to be the same. i'm not sure about a signature. even if one is required she could sign for you. you could just put a note in the shipping instructions about that if you are worried.
i do prefer using newegg for online orders though. they have a pretty huge inventory and decent prices. as far as a letter, what do you mean? i dont receive a letter every month and have pushed over 6 grand through them. do what you want though.