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?
>>> for redundancy its not required to create a etherchannel at the physical switch. because if one port/path fails the traffic will flow through the other one.
But for load balancing its a good idea to aggregate physical ports. Because by doing this we will get aggregate throughput of both ports.
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?
>> its vary based on the storage vendor and storage. its good to go through the vendor best practice guide for iSCSI settings in VMware.
Like this Dell document.