Well, as for the Chinese music ca 1000 AD, you're talking Song dynasty. In fact, it's interesting that you pick this time for Chinese culture, because during the Southern Song period and Jin Dynasty in the north, there was a focus in the Southern Song on cultural matters (intensifying "Chinese" culture), and then when the Mongolian Yuan dynasty was established, Mongolian culture started to seep in. But, nonetheless, the two most common instruments were the GuZheng (古筝) and PiPa (琵琶) though both had been around for a time beforehand.

Example of Guzheng music

Example of PiPa music

As for the Mongolian music, somebody may come around with better answers to this, but Tuvan throat singing may be the closest. Other than that, there was also SanQu (散曲) poetry, which spread first through the Jurchen Jin Dynasty, then through the Song and Mongolian Yuan dynasty.

I hope this post does not violate the rules -- while I can't really give you a definitive answer to any of these (my speciality is Anglophone balladry), I can give you some strong words of caution.

Trying to reconstruct music and performance styles from eras predating recording technology is going to involve a lot of guesswork at best. Moreover, I would be extremely hesitant to use the sources you give above as illustrative of your chosen time periods. The second link you posted above, for instance, was recorded by a self-described metal band. They almost certainly aren't making (or trying to make) an accurate recreation of Persian music from twenty-five hundred years ago -- more likely they are using some of the same scales and perhaps some of the same instruments that have become associated with the area.

Unfortunately, musicians and scholars often have a vested interest in claiming antiquity without justification (for ideological, monetary, or other reasons). It has certainly been common in my field for both specialists and non-specialists to assign antiquity to specimens that can at best be dated to a few hundred years before and can often be definitively dated to as late as the nineteenth or twentieth century. One infamous example is the entirely spurious conclusion by socialist scholar A.L. (Bert) Lloyd in Folksong In England (1967) that a riddle song called "The Cutty Wren" is a violent relic of the Peasant's Rebellion of 1381. Always be wary of similar claims.

However, there are surviving examples of musical notation that date back several thousand years, and there are contiguous musical traditions that can be shown to date back great lengths (like, say, Gamelan in Java), but keep in mind that any modern performance are is going to be filtered through a modern idiom. Even contiguous traditions evolve significantly over time.

Normally we do not allow "throughout history" questions, but as you're being very specific with several time periods, this is allowed. That being said, we also have a homework policy and finding out most of these should be well within the research ability of an older high school student or young college student.

What grade are you, and where have you looked for answers? Which ones are you particularly stuck on? And are you focusing on folk music or "art music?"

Tuvan and Mongolian throat singing is different. Lots of people mix it up, so it's easy to confuse, and "Tuvan throat singing" has become a blanket term for it. What was linked by Jasfss was a Tuvan, from the Republic of Tuva, ethnically Turkic, singing with a Tuvan technique. The instruments, techniques and traditions for Mongolians and Tuvans are different, and both seem to claim, that they invented it. In this example of Mongolian höömii, or this for a more technical demonstration you can hear the constriction is much tighter, the instruments are different, and the famous whistling tune is also notably different. Here's a Tuvan ensemble for comparison.

For more Mongolian musical tradition, look up the Morin-Khuur, which is a very important part of Mongolian culture.

As for Norse music, you have the jaw harp, which has been found in most Scandinavian countries, and seems to be a very old instrument. And any Scandinavian with an interest in musical history will of course know the following two lines: [Drømde mik en drøm i nat um silki ok ærlik pæl] (http://en.wikipedia.org/wiki/Dr%C3%B8mde_mik_en_dr%C3%B8m_i_nat)