If a chess set has pieces which seem to be mini sculptures of faces etc. (like many of the hand-made ones you will find in South Africa), are they considered idols? Did anyone hear of something like this? Sources would be appreciated.
There is definitely no question of Avodah Zarah if they are not worshiped or made for worshiping.
As to the concern of Lo Ta'asun Iti, the prohibition of making even those statues of man not constructed for the purposes of worship, Shulchan Aruch YD 141:10 says that the statue needs to be of a full man in order to be prohibited. A bust with a head but no body, or a statue of a body with no head is excluded from the prohibition. As such I suspect chess pieces are allowed.
Chacham Ovadia Yosef writes in Halichot Olam (vol. 7, p. 281) that purchasing, owning or selling dolls is permissible. He explains that Halacha forbids possessing figures of human beings because they give the appearance of idolatrous articles. When it comes to toy dolls, however, it is clear to all that they serve as toys for children, and are not used as objects of worship. Furthermore, children generally use dolls in a disrespectful manner, throwing them around on the floor, stepping on them, and so on, and therefore they cannot be mistaken for articles of idolatry.
However, if a person receives a trophy with a complete image of a human being, and he wishes to place it on his mantle, this may, indeed, violate the prohibition of possessing images of a human being. One should therefore disfigure the image or remove one of the trophy's body parts, such as an arm or the nose. The Shulchan Aruch rules that the prohibition applies only to complete images of a human being, and therefore once a body part is removed from the trophy one may keep it in his home.
Assuming a trophy is considered something that could be misconstrued as an idol (though it is highly unlikely that anyone in the contemporary western world would do so), some of the chess pieces would likely be subject to the same ruling.
Shevet Ha-Levi is stringent concerning dolls (based on Yoreh De’ah 141).
However, many are lenient, because the doll is clearly a children’s toy, and not something that any self-respecting idolater will worship. This is parallel to the halachah of keilim mevuzim, which are permitted even when they have a tzurah on them, because they are certainly not intended for idolatry.
The common custom is to be lenient in this matter; though this is possibly out of ignorance of the issue, I know many yerei shamayim who are not particular about buying dolls.
If somebody has such dolls in his possession, he must be careful not to “fix” them if they break, for this can be involve a severe prohibition.
See: Shut Oznei Yehoshua (1:13); Yabia Omer (3: Yoreh De’ah 8); Yecheveh Da’as (3:64).
In contrast, Ohr Sameach's "Ask the Rabbi" cites the Chokhmath Adam (85:6) that suggests that nowadays in the western world where there is no longer such a concern of suspected idolatrous uses for these types of objects, ownership alone is not as problematic. Also, see sources cited here.
So, in sum, CYLOR.