Usually the way it works is you get signing bonus with your first paycheck, and then you have to return a prorated amount if you leave before the first year. It's possible they negotiated something better, but unlikely.

Amazon avoids this problem altogether by paying the signing bonus 1/52 with each bi-weekly paycheck for the first two years. They also do the proration on five workdays in a week when it's in their favor, but seven days in a week when it's in your favor, so they win either way.

They would not. And most of these flashy numbers are paid in options, which typically do not begin vesting for 1 year. That bit is negotiable depending on the stock plan, but in any event, certainly no value is given to the employee on day -1 or 0.