Hmm... I don't know what simonwallace is talking about...
1. Yes, you can apply for the waiver outside of the US. The requirements for the waiver are different depending on the basis you are applying (e.g. no objection, hardship)
2. When you apply for H/L/K visa or green card, they will ask you for proofs of being in your home country. You will have to present evidence such as immigration stamps on passport, payroll, transcript, credit card bill, etc.