I'd recommend giving yourself 1 extra week from the point you originally wanted to launch. Make sure everything is finished, and give yourself 1 week to actually use the product. Fix all the little things, and add the extra polish, things you really wish you had time to do before. But don't delay more than a week.
I don't think so. Getting enough traffic to choke a small VPS is possible sooner than you may expect, especially if you have not rooted out all serious bottlenecks (which are often discovered during load testing.)
That all depends on what you haven't done yet. Assuming that all you need to do is tell people about what you've got and the money will come freely and nothing will break, I would just send out a press release announcing your launch.
Load test and optimize user experience. You have one crack at attracting users. If your site is down, or the user experience is sluggish,that's bad news. Make sure you have some external monitoring in place.
I don't know about this lack of sleep bit. I tried it and people have better ideas and do better work when not stressed. I'd rather substitute better planning for lack of sleep.