I have no idea where to start. The ask is to create a tracking log where someone does something, selects from a multi selection lookup column and then a task process is started and assigned to each of those selected from that lookup field. They review something (externally) come back to the list, add their initials and date and the task then goes to another participant where they can do the same and also make comments/notes about what they did and then the task goes back to the first groups. No documents are created. This basically a tracking process with comments based off a multiple selection lookup field. I'm by no means an expert with any of this.
You may want to look at the following features (in rough order)
Hope this helps