These terms, as you know, are all from the linguistic theories of Ferdinand de Saussure. As I understand it, enotes editors aren’t supposed to answer a string of questions, so I’ll give examples of the first two sets of terms.
The signifier is the label, and the signified is the thing being referred to by that label. Taken together, the signifier and signified make up what is called the linguistic sign. An example of a signifier would be “dog.” The corresponding signified (however differently each one of us might imagine it) would belong to a particular set of four-legged mammals that have been work animals and companions for humans for a very, very long time. When wear hear "dog," we do not think of a horse, cow, or cat. We think of a dog.
Synchronic and diachronic are terms that both deal with time (the Greek root “chronos” means time). “Synchronic“ may make you think of “synchronize,” and it should, because they both refer to things happening at the same time. “Diachronic” is the opposite, meaning something like “happening over time” or “happening through time.” You take a synchronic approach to meaning when you look at a specific word in sentence and consider, for example, why that word is used instead of another word. You take a diachronic approach to meaning when you look at the order of all the words that appear in the sentence and compare it to the order of words in the past. The terms have application beyond the study of meaning on the level of the sentence. If you studied some particular use of language among a particular population today, for example, you would be using a synchronic approach. If you studied the changes in use of language within that population over time, you would be using a diachronic approach.
I hope that these definitions and examples get you started!