Identifying Markings on Asian Tea Set?

There is a mark: a circle with the cross in - the Shimazu family crest (the Shimazu mon). The Shimazu clan ruled the Satsuma province in Japan around the time that most of the original items were made. Use the gotheborg.com/.../satsuma.shtml ;
to find more information about Satsuma ware and marks.
Most original items have the maker's signature done by hand. Some more modern copies have the Shimazu crest, but they have been stamped or printed with a machine, they are most likely from mid to late 20th century and worth less value.

The Shimazu mon is accompanied by a signature or mark of the maker. The Kanji (Japanese symbols) will often be the name of the maker or sometimes a number, placing the piece as one of a series of potteries, designed to be displayed in a certain order.
There are no English words on the marking of your set. Many pieces made after the 1940's were marked with "Made in Japan'' or "Japanese Satsuma" on them.
From the beginning the use of the Shimazu mon was meaningful and had to be admitted by the Daimyo. In that case it was always painted in gusu blue, being the right color of the Shimazu mon (cobalt blue was not yet available in Japan). After the shogunate disintegrated and, consequently, no relation exists any longer between the production of pottery and the Shimazu family, the crest was frequently used as a trademark, regardless of its origin and merely as an indication that it is a satsuma-like product. A crest that is depicted in black, gold or red therefore has no relationship with the Shimazu family and it always dates from a period after Edo. Authentic relationships with the Shimazu clan are always in gosu-blue, not in other colors.
One of the obvious differences between porcelain and earthenware pottery is that the former is very thin, which allows you to hold the item and tap it, producing a "ring" sound. Satsumaware is made from clay and earth, this means that they have thicker "walls" and the material will not allow a "ring" when tapped. You can test your Satsuma pieces yourself to see if they will produce a high pitched round when tapped. If you get a dull sound, then you are more likely to have genuine pieces.

One of the best ways to estimate the price is to look at what is selling and see if you can find something similar to your piece.
www.lot-art.com/.../7373-antique_japanese-10.7.21-twent

www.pinterest.ie/.../
The price of a tea set Satsuma Japan porcelain cups dragons from the 19th century is 750 euros www.antiques-delaval.com/.../7292-service-a-the-tasses-porcelaine...

This is Japanese Satsuma Dragonware from the late 1800 (Meiji period). The marking is a family crest; you could try to find it on this website: litaxulingkelley.blogspot.com/.../japanese-porcelain-marks.html

A teapot and creamer/sugar are listed on etsy for $385 USD. I would advise that you get your pieces professionally appraised -- they're not only very beautiful but potentially quite valuable!