1. Yes, you need to be at home (or at least somebody) because you have to sign for it. However, CEVA will call you ahead of time to set up a date & time.
2. It depends where you live and where it's shipped. I would say on an average, about 5 days. After your order has gone through, they would give you an estimate date. That date is real conservative so you should get your tv much sooner than that if it is in stock.
3. If there is something wrong with it (within 30 days), call amazon and they will ship another one to you while picking up the old one.