Sometimes when I add words they don't have Readings and Definitions to train. Can I in some way add those by myself?

You can add the definitions--if you're adding words to a list, there should be an "Add Definition" box you can click. If not, you can always edit the definition by clicking on the word to get the word popup, then clicking "Edit Definition". If there is no definition there, also check "submit as correction" so that we can incorporate your new, awesome definition.

Unless you're creating the word for the first time, though, you can't add a reading. It's strange that you would find many words without them--what kind of words are you adding? You can always submit a correction for them (either from our contact page or the feedback tab when studying) and we'll get the reading added for you.

Does this answer your question, or do I perhaps misunderstand the issue?