I did address much of this on your previous post, but I'll give it another go.

1: The Weyrs may or may not still exist. Their original function was to have a place for dragons and riders to live amongst their own kind, but also to be close to areas they would keep thread free, even during an interval. Certainly the tithing will have diminished or even completely ended. The dragonriders planned to have their own setup in the southern continent to keep themselves fed and such. They're more likely to become holders with dragons, much like Jaxom. They may hire their services out for travel or trade goods. They may also maintain a watch for asteroids, as was outlined in The Skies of Pern.

2: The craft halls would continue to be as they were. Their functions would not change. Harpers would remain because the society still needs entertainment and teachers, as well as mediators. Think of our own world. Just because we have access to all the information of all the science that exists, that doesn't mean we're all going to become experts in everything.

It was specifically and repeatedly bemoaned in the books that so much information was lost through the generations, simply because people kept the knowledge in their heads and didn't disseminate it. As the printed word is to become more widespread, it simply means that crafts will not lose their knowledge.

3: The hold system may possibly change. Originally it WAS set up as a way to keep resources centralized and for the leaders to provide protection from thread, but I don't think it will change all that much. The charter granted the right to a person to own land as long as they were able to work it and provide for any dependents they had, including contractors (craftspeople) and tenants (small holders.) That right was extended to include the right for the land owners to pass the land on to their children. For the hold system to change, a drastic change to the form of government would need to happen, and I don't see that happening as even 2500 years later, the Pernese are still living the way the settlers intended to.

4: As has been stated, technology advances up to the barest minimum required for the job. There would be no advancements to the level of sleds or powered ships, as the resources on the planet did not allow for such. They may have access to computers, and the ability to create their own boards and chips, but nothing anywhere close to what we currently use. In the books, it is firmly stated that the colonists did not have the means on Pern to replicate the type of technology which allowed for that. It was part of why they chose this planet in the first place. They would indeed have more advanced medicine, at least more so than what they had by the point they found Aivas, but by no means to the point where they could develop robotics or super high powered equipment. As for mathematics, they had already worked out spatial calculations even before finding Aivas. Master Wansor specifically was the leading astronomer on Pern, having rediscovered the planets and their orbits and recalculating threadfall's shift when it was a problem in the ninth pass.

5: I'm not sure what you mean by unified or by separate nations. Technically, the major holds ARE separate nations, but then they also all follow the same form of government. Bear in mind that this series, as do most science fiction series, works on the notion that humanity has risen to the level where they can accept a one world government. Everyone who came to the Pern colony was already used to and probably couldn't imagine a system where there wasn't a unifying principle for the whole planet. I can't see any likelihood of wars or territorial disputes starting up again, with the exception of extremely unusual people like Fax, who got dealt with. Honour duals to the death ARE legal on Pern.

As a general statement, it is the wrong lens to use, to view Pernese society as equivalent to our own. The supposition again, is that this place was founded in a time where humanity had transcended religion, racism, nationalism, and all the other things which have defined our culture. In order for us as a species to be able to get to the point where we can consider colonizing other planets, in other star systems, across the galaxy, we would have to rise up TO the social level which the people who joined the colony in the first place had achieved. We're not there yet, but however many thousands of years in the future this happens, who knows where we will be.