Yes. There are two lotteries: one exclusively for people with US Masters or PhD degrees (20000 winners) and one for the rest. If you do have a US advanced degree and don't win the first lottery, you have one more chance in the wider applicant pool.

Yes. And, as alluded to in the article, one of the things the body-shops do to game the system is flood as many applications as possible, knowing that they won't get all of them and not caring which ones they do or don't get.

Perhaps the petition fee should be non-refundable for H1B dependent employers.

No. If you are talking about the H1B lottery, the applications are of a candidate-company-position. When there are too many applications, there is a lottery to select applications that will be examined. After examination, your application can be selected or denied (or they ask for more information). If you are selected, then you are going to work for the company-position of your application. If you pay for the premium process service, the answer of the examination is faster.

yes, your understanding is correct. The odd was 1 out of 3 this year I think.

it only proves again that H1B process is seriously broken. they must have sorted people by salary in the offer picking higher paid.