That's because it is not required on vehicles that are fitted with an "EC specification" licence plate that has the country identifier at the far left edge of the licence plate. But it still is very much required (by the Geneva Convention on Road Traffic (1949) and Vienna Convention on Road Traffic (1968) for vehicles that do not display a EC specification plate, such as the original poster's North American motorcycle.
That's a tricky question that I don't want to try to answer because of the risk of misleading you. Countries have limits on both the length of stay of a single continuous visit and the total accumulated length of stay in their country (or their 'visa area', such as the Schengen Area). I believe that the Schengen area countries impose a limit of 90 days within any 180 day period for stay in the area, regardless of the number of times you go in and out. So you are going to need to do your own due diligence in that respect, but it sounds like with your one month on, one month off work schedule you might be able to avoid falling foul of that limitation if you plan carefully. Be aware that the whole Schengen area immigration system is computerized and interconnected, and the border officials do pay attention to that "90 in 180" limit.
I apologize if I have offended you. I admit that my 'throwaway comment' (a fairly accurate description) may have painted some -stan countries with an unwarranted brush.

I have, though, spent (cumulatively) years living and working in various -stan countries, such as Pakistan, Afghanistan, and Kazakhstan, and based on my first hand experience with government regulations and government administration in those countries, they are very difficult places to operate in and I don't recommend them to travellers who want to enter with their own vehicle and travel independently. It is quite possible that if a visitor entered with an organized tour, or with a carefully pre-planned itinerary that did not include bringing their own vehicle in, that they could enjoy a pleasant visit.

I do acknowledge the truth of your comment that the people in those countries can be very nice. But the government practices and administrative practices that visitors need to put up with are, in many cases, truly fecked up. Consider, for example, Russia. The individual people are darn nice. But the government practices impose an insurmountable barrier on visitors. That concept is what prompted my comment.

Michael