With that setup, you have quorum as long a node 1 is online. So yes, you can start/stop/edit while the second node is offline. There is no risk for split-brain if you keep the votes that way.
Btw, this is easy to test...
Proxmox VE is a bare-metal hypervisor platform aimed at IT professionals and system administrators. It is not a product or service directed at children ...
a.) There are no initial or incremental/differential backups - only deduplicated backups.
b.) After stop/start, backup needs to read the whole disks, but backup are still fully deduplicated.
c.) backup data is deduplicated at the server side.