1. An illustration from the Warring States period (ended 221 BCE) shows a two decked Chinese warship with rowers on rhe lower deck and a fighting deck above them with men armed with halberds and short swords. T his looks very much like a rowed version of the medieval fighting Cog, designed to close with and board the enemy. However, the evidence available indicates most of these ships were river craft, not sea-going. By the Sui Dynasty (584 CE) 5-decked "tower ships" are being built, but again, there is only record of them used as river and lake craft, not oceanic.
Absence of evidence does not equal evidence of absence, as they say. While the Chinese were building ships as big as anything actually used in battle in the Mediterranean by at least the end of the Han Dynasty, we simply do not have direct evidence they were fighting with them in the ocean. I think it is highly likely, simply because by the end of the Han (200 CE) Chinese traders were sailing at least as far as the Mekong in Southeast Asia, where they met with Roman ambassadors, and traders need protection.
2. As
@Zaarin posted, it has been suggested that the Hsiong-Nu and Huns were the same people, but since we don't have any DNA evidence (yet) or linguistic evidence to link them, the connection has to be listed as speculation only.
One thing that confuses the question is that numerous steppe people migrated west out of the Altai either voluntarily or involuntarily (pushed), ranging from the Yuezhi to various later Turkic groups and possibly including Hsiong-Nu factions and the Huns, but they are nearly impossible to tell apart from archeological finds alone: everybody used the same horse tack, weapons, wore similar clothing and were composed of groups with multi-ethnic composition, so horse or human skeletons and burial goods aren't usually enough to identify any individual or group for certain.