1,大概到B大學上班前多長時間,讓B大學遞交H1申請?
You can sign document and make sure your starting date. B university will know how to do it, you don't need care. The new H1 visa will tell you the starting date.
2,如果B大H1申請下來,而A大學的工作尚未結束,能否不按批準書上的日期,推後上崗?(如:H1批準3月1日可到B大上班,但各方同意後,到5月1號才到B大學報道,可否?);
Yes, you can, but you need talk with your new employer.
3, 聽說隻要USCIS收到B大學的H1申請,就可以上崗,是否屬實?此情況是不是隻在同一大學內才行?
You need get H1 visa, or H1 receipt notice before you start your work. (some university ca do what you say, you can work just the university filing documents to USCIS).