The #1 question
Unfortunately it's not an easy question to answer.
The major reason is that there's not a whole lot of specific evidence to go on. There are very few surviving sets of beads; none, as far as I know, are complete any earlier than the late 15th or early 16th century. Evidence from portraits is almost entirely from the 15th and 16th centuries as well, and I've only begun to collect evidence from wills and other documents. I am sure there's lots more evidence out there, but it seems to be very spotty and it doesn't seem that anyone's collected it all in one place.
I can say that what I have isn't nearly enough yet to let me detect any differences according to what country something comes from. It may very well be that there isn't much difference by country; certainly in clothing fashions, there are times and places where people in several widely spread countries are wearing pretty much the same things. On the other hand, I may just not have enough data for trends or differences to become apparent. I do see special "types" being prevalent at certain times and places -- the large coral rosaries in 16th-century Germany, for instance. But aside from those, I really can't say anything useful about (for instance) French rosaries versus English rosaries versus Dutch rosaries.
There is also, of course, not just one "correct" type for a given time and place. We have documentation in the 15th century, for instance, for straight strings of twenty beads or so and loops of fifty with "gauds" or marker beads, among other types. Even after the Council of Trent (1569) we see several different types in use: short strings of ten beads, loops of fifty or sixty with gauds and a cross, and loops of fifty with the "tail" of five added beads that are universal on today's rosaries.
However, clearly there's a need for information by century, even if it turns out that the information includes several "right answers" instead of just one. So in the medium-to-long-range plans for the Paternoster-Row website, a series of "century pages" or the equivalent will definitely have a place.
I'm really just at the beginning of trying to tap into all the information that is out there, so who knows what I will find!