Ask for POE for TN renew. If I apply for H1B in Apr, is it ok?

My TN expires in June, and I applied renew TN in Jan. Now they ask for POE (no intention of establishing permanent residence). The problem is that I have an approved I-140.

If I apply for H1B, the starting date have to be 10/01/07.There is a gap between my TN expire date (06/19/07) and H1B starting date. Can I work during this period?

What's going to happen if I apply H1B before I my POE for TN? Does this cacel my TN application automaticly.

Thank you for your info and advice.