However I also found rather confusing properties of monads, like they
where "living mirrors of the universe" [...] Is there a notion of time
/ order of actions / cause associated with monads?
Monads mirror – each one under its own aspect – the entire universe, and these mirrorings involve not only the present, but also past and virtual future states. But this must not be understood as causal influence or interaction, because this would contradict their being "fensterlos" (window-less) and their existence as substantial units. What is perceived as effect is really based on an ideal influence established by God, who by thinking through all possible states and courses of the world, accounts for every substance. This is the principle of "prästabilierte Harmonie".
[...] and can be sleeping or awake. So is the idea really that those
monads (of which I think like "atoms") are like "minds" or living
Leibniz uses the term Monad for individual substances, which have no parts. ("La Monade ... n'est autre chose, qu'une substance simple, qui entre dans les composés; simple, c'est à dire, sans parties") This is a continuation of, and includes, scholastic traditions ("ens et unum convertuntur").
This is in contrast to Descartes' dualism. Leibniz takes the modern concept of individuals, well-founded in Descartes' cogito argument, and lifts the soul-having "I" to being the substance. The infinite number of ideal, individual, and dynamic substances, which all mirror the entire universe, is Leibniz' answer to Descartes' dualism, Spinoza's monism, and Gassendi's atomism.
Only organic creatures (humans, animals, plants) are such units, not corpora which are mere aggregates and phaenomena. Decomposition of composites will, according to Leibniz, not lead to material units, because continuous division of corpora will not lead to something that could be called "unum per se". They are "metaphysische Punkte" (metaphysical points), can neither be made or destroyed physically, and are all different.
Monads are dynamic, and only differ by their inner states, their "Perzeptionen" (perceptions). Their dynamicism is due to an inner urge ("appetition"), which advances them from perception to perception. Leibniz calls monads, whose perception is accompanied by recollection souls. (So, in contrast to Descartes, according to Leibniz, animals have souls) Monads which represent "die äußeren Dinge" (the outer things) must be distinguished from "Apperzeptionen", which means self-awareness or reflexive cognition. Monads capable of this are called "vernünftige Seelen" or "Geister" (intelligent souls or spirits, "animae"). Now, there is a hierarchy of monads with regard to their apperceptions: From "schlummernden" (slumbering) up to the omniscient monad, the "monas monadum" (monad of monads) – God. Somewhere in between are animal and spirit monads. Also, every monad has a dedicated corpus, a body which is itself assembled from parts, which themselves have their dedicated monads, lower in the hierarchy. Only the monas monadum exists without one.
All in all, this is a very difficult topic. I hope I was of any help, and did not add to your confusion. I would not claim that I understand Leibniz' system myself in its entirety.
Source: Historisches Wörterbuch der Philosophie, Bd. 6: Monade, J. Ritter et al., 1971