Not after bite. The bug will not remain on the skin, but rather its evidence will be a very itchy small firm red bump where you were bitten.
Usually not. The missouri dept. Of conservation says chiggers are baby mites that can only bite through areas of thinner, tender skin. Chiggers bite to inject saliva to dissolve flesh and eat it up. They do not suck blood nor burrow into the skin. They are less than 1/150th of an inch, so are almost invisible, but several together can look like a red dot. Many can be on a person at one time.