To my current understanding, German has three word moods and for each mood the following tenses:
Since imperative is a mood, does there exist 'past' imperative? Would that ever be used? It seems a bit non intuitive to me since imperative would be like giving an immediate action. So, would it be an 'order' in the past?
Grammarians call the imperative a mood, but I'm not sure that's really a helpful way to classify it. As mentioned in the comments, it does not have a tense. You can classify sentences according to various tense, mood, aspect, etc., and ask philosophical questions about whether certain combinations exist or not. But grammar is only a description of language, a theory of which combinations of words can to said in a given language. If grammar predicts combinations that aren't possible then it's grammar that's wrong, not the language. The imperative is something of an exceptional case because some combinations can't occur in practice. For example there is no first person singular imperative. I suppose you could invent one for people who like to talk to themselves, but languages tend not to have unnecessary and unhelpful features. Similarly, until someone invents a time machine, a past tense imperative doesn't seem too practical.
There basically is just one imperative. However, if a tense if constructed using an auxiliary verb, you can technically form an imperative in that tense by applying the imperative to the auxiliary. Wiktionary even lists an “Imperativ Perfekt”, but also marks it as “ungebräuchlich“. I would question the usefulness of that concept, though.
