Can H4 to H1b with COS be filed a few days after Oct1st?

[h1bques]

I have a question about H4 to H1b with COS. Consider this situation and kindly let me know if it is feasible.

I am residing out of US and my H1B petition has been approved WITHOUT COS. I come to US on a H4 stamp before October 1st which is my H1b start date.

1) I want to know if H1B with consular processing will start on Oct 1st even if there is no H1B stamping but I only have H4 stamp?

2) Can I continue staying on H4 and apply for COS to H1b (on an approved H1b with CP) at a date later than Oct 1st, say Oct 20th? If yes, will I be on H4 status until the COS is approved?