I want to create artificial ecosystem.
I don't want to do it in random way like "We have cats but lets name them kads. They live in forest... of mushrooms. And there is a river. I think it is enough."
I look for some manual which enumerates important parts of ecosystem which should be think about: energy cycle, chemical cycle, food webs and so on.
Or at least a good description of some existing ecosystem with separating by different aspects.
Um this question is a little unclear and or too broad but I doubt you will able to refine it so I will give you some pointers.
As far as manuals go in this case, the manuals would be biology, geology, and maybe chemistry & meteorology.
But to simplify all of those complexities I will mention the broad strokes of what to focus on:
Energy/nutrients - In all ecosystems energy is largely recycled but is always inevitably lost through heat. The first part of this is defining what are the primary energy inputs for your ecosystem ex solar or hydrothermal. From there you define who transforms that energy into nutrients (ex plants), who eats those nutrients(ex predators), what eats them(ex apex predators), how is waste recycled back into the system(ex mushrooms and worms) (these are huge generalizations). The available chemistry of the system is also a large factor but I will skip over this for the sake of brevity. Suffice it to say we are carbon based lifeforms, plants take in atmospheric CO2 and store energy in sugars and waste O2 back into the air, we eat ~sugars and breath in O2 and waste CO2 back into the air.
Environment - The majority of evolutional adaptations are focused at optimizing an organisms success to environmental challenges. Example skin and hair protect against UV radiation, cold, abrasive damage (like from rocks or weeds), blunt force damage, toxins, etc while sweat protects against heat.
Catastrophe - This is a subset to environment but encompasses more wild card events that drive extinctions/ super selection events. This can be the emergence of toxins that an ecosystem doesn't know how to neutralize (ex micro plastics or even oxygen for early biomes). This can be nuclear winters caused by meteor strikes that blot out the sun for years which favor flora whose seeds can last for years before conditions become favorable.
Reproduction - I'm putting this in for posterity because its sort of a duh rule. But the ultimate accomplishment for an organism is that it successfully reproduces and passes on its genes. This is important because this evolutionally means that your traits and adaptations were correct.
The first two factors are the largest drivers of how species evolve and subsequently how ecosystems form. The third factor is meant to tie in how pollution/ chemical imbalance can radically alter ecosystems and drive or whittle diversity.
So to sum it up and generalize it even further. You start with external input energies to the system. You consider the challenges a creature has to overcome to store that energy and reproduce. You can then consider what can eat them and how they eat them. From there you just keep building up how creatures overcome challenges to obtain food and reproduce. Note, by obtain food I don't necessarily mean hunt, for instance a mushroom could spread its spores such that they stick to the fur of passing predators that then get deposited on felled prey thus achieving food obtainment and reproduction.
Ecosystems are deceptively simple to set up. You don't need to audit energy, nitrogen, carbon, etc.
If there are cats in your forest, you need enough rodentia and avia for them to eat. To support the avian and rodent population you need insects, seeds, and fruit. To support the insects and the plants you need offal, death, and decay.
If there is an explosion in the rodents' food supply, as there is in India every 47-ish years, the rodent population will explode (into a plague in India's case). If this is the food source for your cats and birds then those populations will also increase rapidly -- followed by a die-off when they have eaten all the rodents who can no longer reproduce quickly enough to feed the cats because all their food is also gone.
So, if you have a particular apex predator that you want in your world then you can start top-down -- what does that predator eat, what does its prey eat, and so-on.
Is it a pack animal? Then it probably includes very large animals in its diet; prey which is too large for a single member of the pack to kill on its own -- that's why the species lives in a pack. Solitary predators tend to be very powerful but can only take down prey which are twice or thrice their mass.
If you have a useful omnivorous or herbivorous middle-cycle animal you want in your world then not only do you need a food source to support it, but you have to have a predator above it to maintain a balanced population, otherwise you will be overrun by this animal.
Rabbits, for example, can literally have a maximum of 12 litters of kits per year! One female can easily produce 5 dozen offspring every year. That feeds a lot of foxes, assuming that you have enough roughage to feed the rabbits.
Desert ecologies can be very interesting and challenging. Most deserts aren't large enough to be devoid of life, but the deeper you go into a desert the more sterile it gets. You won't find a wide variety of large animals in the desert, and when you do they will almost always be herbivorous specialists. If they're carnivores then they're almost always nocturnal.
I get pretty involved in some of my simulations: how many calories in plant nectar or in a particular nut, how many calories in this type of bug, how many calories does a particular predator animal need to thrive versus how many to just survive, what type of insect is needed to pollinate a particular type of plant, etc. I do that just because it's interesting and fun to watch, but you don't have to do that to create a believable ecology.
One of the biggest problems I had with many Dungeon Masters was the number of dragons they have in their worlds -- they were all over the damn place! Everyone had a flippin' dragon! One country had an entire dragon air force!
Impressive, but what do they eat?!? A dragon is a very high-energy animal -- it's difficult to keep a dragon without the surrounding countryside showing the effects of it! One of my players once asked me why dragons always live in some "waste" somewhere. I laughed and said, "It wasn't a waste before the dragon got there!" Which later led into a humorous interaction when the dragon finally introduced himself, but that's a story for Quora.
The point is that it doesn't take much to create a believable, workable, and even flexible ecology. And it's worth the effort: a believable ecology makes for a much more enjoyable world. Just remember that at its most basic level your ecology will probably be powered by death and decay. No death, no decay, no nutrients, no plants, no insects, no anything else.
There is more complexity to ecosystems than most people realize. Even very small changes can decimate populations and lead to ecosystem collapse. I'm sure there are some good college textbooks out there that talk about ecosystems in various climates, topography, and so on.
But I would start off with Rachel Carson's book Silent Spring. It's older but still quite relevant. Her focus is on what happens when humans make one seemingly small change. Most of the book is about using pesticides to kill insects. But the ramifications are enormous and further than you might imagine. Ditto things like clearing brush around creeks, something humans do all the time. Everything matters.
It's not that you can't have a viable ecosystem built around any number of factors. It's that change brings chaos (and not the cool artsy kind). Understanding how those changes affect the ecosystem will help you understand how they work. And that will help you in creating your own.
