1) In order to get NIC redundancy and/or load balancing working in ESXi, do I have to aggregate the two physical ports on the switch(s) that connect to the the two physical ports that connect to the vSwitch?
No you do not need to configure etherchannel/LACP but it will depend on the type of Load Balancing you select on the ESXi host - if you use default you will not need configure Etehrchannel/LACP since the traffice for each virtual network interface will only com ove a single physical port but you will still the reiciliency in case if one of the physical nics fails the traffic will then go out the remaining port
If you select the IP Hash load balancing you will then need to implement Etherchannel/LACP on your physical switch since traffice can come form any physical port in the team.
2) With NIC teaming, I see, for the management network, how having one active adapter and one standby adapter works fine, but, for the iSCSI network, wouldn't I want both adapters to be active to double the bandwidth?
Well onece again it is going to depend on the Load Balancing methodology you select but you will never be able to bond the physical ports to get the full 2 GB =
I have also moved this to a more appropriate forum -