1. If we sign the least today - do we have access to move furniture in ASAP?
No, the deposit today is only a holding deposit. The lease starts on 11/1
2. If not, can we sign the lease a little smaller deposit and pay remainder closer to the 1st?
That's not what we agreed to.
We can exchange key and nov. rent on 10/31 (or 10/30, 10/29... negotiate) so you can have whole day on 11/1 to move in.