If the consulting company applies COS, then you need to work either from October 1 or from approved date after October.
2.Yes you can continue on L1B but you need to invalidate COS in case if they apply by just leaving US and come back on L1B between Sep 20 - October 1 week. In case if they apply any COS this will invalidate your COS.
You can hold H1 and you can join them if they agree or other employer by applying cap exempt transfer if you have petition.
Please refer the below question which was answered by Saurabh.
Is there any way the consultancy apply for my H1B this year without COS?
By this way I can work on my L1B and change the employer when I find some other employer!