The related words you describe include nouns, verbs, adjectives and adverbs, in English it is quite easy to create a verb from a noun (basically you place 'to' in front of the noun to get the infinitive and generate regular cases and other aspects from there).
For example if there was a new noun "flub" you could have the new verb "to flub" with present continuous "flubbing", past participle "flubbed" and so on. You could also create the adjective "flubbish" (like a flub) and the adverb "flubbishly" (in the manner of a flub, whatever that might be). This is the basis of forming the family of words that you are talking about.
Unfortunately there are two problems with this approach when you are thinking about existing words:
Firstly there are quite a lot of verbs which are irregular in some way; a good example is "blood" for which the normal verb is "to bleed" not "to blood" (there is a verb "to blood" but it is quite rare and it doesn't mean to let blood out of your body). There are other verbs which don't have the regular structure.
Secondly not all words have only one meaning. For example the noun "stick" means a long thin piece of something (usually wood and often still with the bark on it) but "to stick" has nothing to do with long thin pieces of stuff and means "to adhere". This means that the adjective "sticky" and the related noun "stickiness" are related to the verb meaning "to adhere" and not to the noun meaning pieces of wood. This gives us the English riddle "What's brown and sticky?" With the answer "A stick"
These are examples of the difficulty of finding a tool to do what you asked, whatever any logical tool tells you has to be checked against the real language for anomalies and there is no way to find the anomalies by logical thought. I don't believe that you will find a logical tool to do this reliably.