-If you had never been H1 before, you can not work until Oct. 1, the date when the H1 is effective. Thus, you have to keep your F1 status valid at least until Sept. 21.
但是不知道f1转换h1b之间的这段时间是不是OOS,
-Yes. See above.
会不会影响将来回国签证和绿卡申请?
-Possible, but hard to say.
是不是中途休学,f1就即刻失效,没有F1的60天grace period了呀?
-Correct.
如果f1即刻失效的话,是不是到summer学期结束, 就没身份了,而i797A只给了authority stay,应此整个九月的身份还是OOS了?
-Correct.