One Hard Drive to backup two Macs with Time Machine, then recover from one, then the other?
It is possible to use an external drive to back up two Macs via Time Machine. Per this thread, the backups will be stored separately, without any special setup needed.
Per pulling specific files from another Time Machine backup, you may want to refer to this thread. It should be doable to search that backup volume without having to install the entire backup onto another machine using the restore feature.