I will leave the second question to someone much more familiar with East Asian literature, but for your first question, yes, there certainly was some interest in products that arrived from the west and the countries that produced them. Chinese merchants and travellers reported what they saw over in the west, and although there aren’t any first-hand accounts from people who had actually visited the west (like there are for Marco Polo, or the numerous other western travellers who are maybe more reliable), there are a few collections of reports, dating all the way back to the earliest contact between China and Rome in the 2nd century.

There’s one collection of reports, Zhu Fan Zhi (“Gazeteer of Foreign Lands”), written around 1225 by Zhao Ruguo, who was the maritime trade inspector in Quanzhou under the Song Dynasty. He incorporated a lot of material from the older reports (including the 12th-century Lingwai Daida). This is the same period where Western Europe became more interested in China, since they were hearing early reports of the Mongols and hoped there might be an opportunity for an alliance against the Muslim states in the Near East. Eventually the Mongols showed in Europe as well, to everyone’s terror. By the time Western travellers and missionaries (including Polo) started showing up in China, the Mongols had also conquered the Song.

European accounts sometimes list the types of products they imported from the east - the one I’m most familiar with, from crusader Jerusalem (of course), names all sorts of things that Europeans purchased from neighbouring Muslim territory but also likely as far away as India and China. The Zhu Fan Zhi does essentially the same thing, and at almost the exactly the same time period, just from the other end of the supply chain.

The Chinese act the time of the Song dynasty knew of the Roman Empire (“Daqin”) and of the Arab empires in between (“Dashi”). Zhao probably had no idea of the local politics in 1225 though, since his information mostly came from much older books and not personal experience (and probably not even the experience of merchants who had been there). Daqin is probably actually Syria since Zhao apparently thought Antioch is the capital city. The Middle East had been conquered by Arabs, then Turks, then European crusaders, and crusaders were ruling in Constantinople in 1225 as well. But regardless of who was in charge over there, the Song imported

“opaque glass, coral, gold ore, flowery brocade, plain cotton cloth, red agate, and pearls”

Zhao also mentions “rhinoceros horn”, although it’s not exactly clear what that means.since there were no rhinoceroses there. In another passage he mentions “Lumei”, which is probably the Chinese pronunciation of “Rome”, i.e. maybe Anatolia, the Byzantine Empire, the Sultanate of Rum, the crusaders in Constantinople, or possible even the Kingdom of Georgia. Lumei produces

“sea silk, yuenuo cotton cloth embroidered with gold words, brocade with alternating threads of gold and silk, bezoar stones, oak nut galls, rosewater, champak flowers, liquid storax, borax, and high-grade opaque glass with engraved flowers. The local households like breeding camels, horses, and dogs.”

Even further to the west were the lands of Sicily (including an account of an eruption of Mt. Etna), which was part of Lumei. There was also Egypt (including a description of the annual Nile flood), and North Africa possibly as far west as Morocco, which were part of Dashi. Zhao had more up-to-date information about Dashi since the Song had more regular contact with Muslim merchants, although he sometimes seems to confuse Baghdad and Cairo. Products that they received from Dashi included

“pearls, ivory, rhinoceros horn, frankincense, ambergris, costus, cloves, nutmeg, benzoin, aloe, myrrh, dragon's blood, asafetida, civet oil, borax, opaque glass, transparent glass, giant clams, coral trees (i.e., red coral), cat's eye gems, champak flowers, rosewater, oak nut galls, beeswax, soft brocade with gold weave, camel-hair cloth, Tūla cotton, and exotic satin.”

According to Zhao, trade with the Arab world mostly came through the Indian Ocean, through modern Thailand and Indonesia, and from there into southern China, rather than overland, but that presumably reflects his own position as inspector in Quanzhou on the coast of the South China Sea. Most of the Zhu Fan Zhi deals with maritime trade with the modern Philippines, Indonesia, Thailand, India, Arabia, and the east coast of Africa since those areas delivered the most trade to Quanzhou. None of the overland trade officials wrote a report like this, unfortunately!

Sources:

There are some previous answers about the Romans and the Silk Road:

Why didn't Romans take a ship to the far east? by u/Tiako

What led to the end of the Silk Road? by u/Sandafluffoid

How "Busy" was the Silk Road at its most used point in History? by u/anchaescastilla

Was there contact between the Byzantines and the Chinese? by myself

The Zhu Fan Zhi is translated in:

Chau Ju-Kua: His Work on the Chinese and Arab Trade in the Twelfth and Thirteenth Centuries, entitled Chu-fan-chi, trans. Friedrich Hirth and W.W. Rockhill (St. Petersburg, 1911)

But that's quite old and out of date, and here I've been using a more recent translation A Chinese Gazetteer of Foreign Lands by Shao-yun Yang, which is online

See also Chen Zhi-Qiang, “Narrative Materials about the Byzantines in Chinese Sources”, in John Burke, ed., Byzantine Narrative: Papers in Honour of Roger Scot (Brill, 2006)