Back to normal again, but still feeling a little like 'death warmed over' as they say! Thanks again for being so understanding.
First, before I get your hopes up, your beautiful Chinese vase is not that old, despite what your exchange student may have hinted or implied. It dates to the last quarter of the 20th century at the oldest, but you are quite right to call it celadon. Mostly any ceramic object from Asia this sea-green color is called celadon, though the word is also used to describe both a glaze and a type of ware as well as a color.
In its original and purest sense it's a type of porcelain-like stoneware that was made in the Longquan area of Zhejiang province in China which reached its peak of perfection during the Yuan dynasty (1271 - 1368) and early Ming and looked like this:
It was typically carved before firing, while the clay was leather hard, glazed and fired, as was the process to make your vase. The resulting decorative effect was hugely admired and sought after by kings and emperors and warlords, not only because it looked jewel-like and expensive, but also because of the belief that the green had magical properties that would help remove poisons from food. Indeed it was believed the green would change color in the presence of poison. Also, because it resembled the color & hardness of jade, a material considered by the Chinese more precious than diamonds or gold, it was admired and greatly sought after simply for that reason too.
"Celadon" is also used to describe any kind of high fired green ware in general, known as qingci, fired in a reducing atmosphere (no oxygen) kiln that causes iron oxide in the glaze to turn green rather than yellow or brown which it would normally do.
It's also used do describe certain types of glassy green glaze that are often also deliberately crazed -as is the case with yours- by accelerating the cooling process after firing, which causes the clay and glaze to contract at different rates and create a crackle, thus giving the impression it's crazed with age.
Ceramics of this nature are of recent origin and are currently produced by truly thousands of mom & pop potteries throughout Asia, particularly in Thailand, Korea, China and Japan. Most of it is unmarked. In China here's no tradition of a potter putting his name on the bot***** *****ke there is here in the west. This is because in the old days making porcelain was a team effort that required a highly specialized division of labor involving scores of individuals to make a single item, from the guy who spent weeks grinding blue lapis rock into paste to make cobalt blue enamel, to the the guy leading teams of water buffalo around and around the clay pit to trample the clay for days in order to condition it for firing. Others who filtered the clay to remove sand and larger particles, those who carted and stacked it for weathering and that was before the throwing of the pot on the wheel was even begun, let alone the decoration and the firing and the shipping to markets all over the world.
So factory or pottery marks like these are a relatively recent phenomenon, if there at all, which does help confirm the recent origin of yours. Because they are so recent, there's really no register or reference work available in the west that covers these marks as yet, nor do collectors pay much attention to them. There are no 'names' that are particularly known about or collected here in West yet, and this pottery isn't old enough to have accumulated any premium for being antique or vintage. It's still being produced in huge and unknowable quantities and sells purely on its decorative appeal.
To add to the confusion, where marks do occur, as here, they usually pose more questions than answers. Lettering that's created in cameo, like this, then covered in glaze is notoriously prone to being corrupted and obscured during firing. Incised or impressed marks are usually more readable.
So I'm not surprised your Chinese exchange student was struggling, and in a way I'm glad she was because it helps when I also tell you that many of these characters are illegible or too ambiguous to make anything of them. Also, where the stroke lines of the characters have been blotted out, the crazing just adds to the problem by implying spurious lines where there shouldn't be.
The best I can do as a transcription is.
But none of that pulls up anything that helps with a translation or a maker.
So, the message here is that you should enjoy your vase for what it is, a very decorative example of recently made, hand-carved celadon, in a beautifully crafted floral pattern above a lappet band arranged around the lower register.
As for value, if you saw it for sale in a vintage or consignment store, not a whole lot, perhaps $60 - $100 at the most for a piece this size.
I do hope this helps answer at least some of your question and please feel free to ask if you'd like me to explain or expand on any of the above, I would be glad to.