Fair on the first point, I’ll adjust the text to clarify the need for a BS.
On the second point, first claim, you can be in an EB-1 queue without an H1-B (e.g. OPT or TN [1]). On the second claim, I admit to not knowing someone who is in the queue and in the lottery but they’re on TN, preparing materials for an EB-1 and applying for an H1-B. My understanding was that they’d apply for both concurrently (due to the EB queue period), but I have no references to back me up.
[1] If you were born in China and then immigrated to Canada, you’re still in the China queue for EB.