1,大概到B大学上班前多长时间,让B大学递交H1申请?
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申请下来,而A大学的工作尚未结束,能否不按批准书上的日期,推后上岗?(如:H1批准3月1日可到B大上班,但各方同意后,到5月1号才到B大学报道,可否?);
Yes, you can, but you need talk with your new employer.
3, 听说只要USCIS收到B大学的H1申请,就可以上岗,是否属实?此情况是不是只在同一大学内才行?
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).