The Verbal section of the GRE requires you to have good knowledge of words from the perspective of using them in the right context. You will not be tested on the meaning/definition of the word. Using the words appropriately in the given context is as important as remembering them.
The Vocabulary tests in WordBot test your understanding of this. The tests are designed to evaluate your understanding of the words along with their synonyms, antonyms, usage, and so on. So based on your SFA's suggestion, you can take the tests.
As of now, you can take tests for all the words that you have learned, irrespective of the word list it is listed under. We are in the process of modifying the logic to enable you to take tests on words of a word list
Yes, you can take a test for the words you've not seen by clicking on Not Seen label in the test section.