The FAA has their rules and then the Office of the Chief Counsel of the FAA will answer questions about them and give their interpretation. Since they are the folks that will write the violation, their thoughts matter.
You can put anything you you want in your logbook. However, if you use improperly logged events to show currency it will cause problems.
1. Your understanding is correct as explained by the the FAA lawyers. You need to separate "operate" and "manipulate." to count for currency, you have to be the "sole manipulator" of the the controls. Actually have your hands on the yoke.
2. Yes both can log it. I don't know what you mean by "that rule is no longer effective." Remember, operate v. manipulate.
3. Again, the the better answer is you must manipulate the controls through the landing.