Periodization

Maybe I'm not understanding part of your question, but periodization, to me, is having specific time frames to focus on specific aspects of training.

Being a runner, I would have a build period, a hill/strength period, a speed period, and a race period.  Mileage for each varies, yes, but so does the intensity.  The first phase is more miles, but at a generally easier pace, the hill period starts to increase the intensity on some of the runs, but will only slightly reduce the mileage, and may keep it the same.  The speed and race periods show lower total miles, but involve much higher intensities. 

Seems like what you are asking is about rest/recovery weeks if I read your question right not really about periodization.

You need them as you absorb your training when you rest ie improve as your body adapts to the stress you placed on it training. You may feel great this week but you need to look 6 months out..you can't always be on and not let your body rebuild and recover.

Most folks do 3 weeks of regular training based on where they are in their training cycle and then do 1 week rest. I do 2 weeks/1 week as I seem to need more rest and I do better on that plan.

Rest weeks for me have lower volume and also no intensity everything is aerobic. My rest weeks this year are more training than my regular weeks were 2 years ago so everything is relative to where you are. 

No worries.

As for a rest week....  Depends on the person.  As Kathy mentioned, she does a 2/1.  I've seen training plans that have a small step-back on week 4, and a bigger one on week 8.  I've done alright with minimal reductions, too, but I was doing a much easier pace overall.  So in some respect, I think it also depends on what training cycle you're in (see how I tied all that other stuff together?  Sweet...).

Ultimately, it's somewhat an experiment of one.  There are general training guidelines to follow to get you started, but you'll learn what volumes your body can handle.

If you're unsure about things, I think the best thing you can do is find a plan to match your goals, track your progress and how your body responds to it, and modify it based on that feedback.

For triathlon training, I go 3 build / 1 recovery.

I generally take just the run volume down (by as much as 40%) as it seems to take the most toll on me.  I keep the intensity low (no intervals, speedwork, etc.) across all three disciplines and no weight training that week.  I maintain bike and swim volume, but again only zone 1 and zone 2 training.

For marathon training, I go 2 build / 1 recovery.  During recovery only zone 1 & 2 stuff, maybe one fairly easy tempo run that week.

Note: I'm a 37 year-old on my 2nd year of endurance training.