Why did Adam need to tend the garden in genesis 2:15. Is the biocycle a sinful process?

Your assumption that prior to sin nothing died, needs to be reviewed in the light of Gen 1: 27-28 :

So God created mankind in his own image, in the image of God he created them; male and female he created them. God blessed them and said to them, “Be fruitful and increase in number; fill the earth and subdue it. Rule over the fish in the sea and the birds in the sky and over every living creature that moves on the ground.”

Physical death was, and is the inevitable outcome of `getting multiplied in number 'so that one generation could leave their place for the future ones to fill in. With no death taking place, and new generations being born, say after each 20 years'gap, it would only take a few centuries for human beings to reach a catastrophic number. Remember that man was blessed to multiply, even before he thought of sinning. But then, it would be safe to say that the sin made life (and physical death) hard for Adam and Eve in that he was made to toil and sweat for bread, and she, to deliver her children in pain .

God first prepared a garden, in the east of an area called Eden, and then placed the man in it. He was commissioned with spreading that garden outside and beyond the existing area of the garden. This is a simple, straightforward explanation as to why Adam needed to get involved in horticulture. Here is what the account states in chapter 2:

"When the Lord God made the earth and the heavens - and no shrub of the field had yet appeared on the field and no plant of the field had yet sprung up, for the Lord God had not sent rain on the earth and there was no man to work the ground, but streams came up from the earth and watered the whole surface of the ground - the Lord God formed the man from the dust of the ground and breathed into his nostrils the breath of life, and the man became a living being.

Now, the Lord God had planted a garden in the east, in Eden; and there he put the man he had formed... The Lord God took the man and put him in the Garden of Eden to work it and take care of it." (Genesis 2:1-15)

Anybody who has a garden knows that unless they take care of it, it will become overgrown. And when a beautiful garden is meant to be extended, then there's plenty work to be done!

Further, the matter of food for what would, in time become a family of humans, required paying attention to the seeds that had not yet become the plants that grow in a field. Grain, for example, would need to be cultivated, to eat alongside the fruit and vegetables already in situ.

The biocycle, as created by God at the beginning, was perfectly balanced to do what it was designed to do - give food in season. Winter was one of the seasons decreed by God, even before man was created, and that is when we see biological changes with plants that require the decay of, for example, apples and blackberries, so that their seed can start to grow into fresh plants. This also calls for worms and micro-organisms to enable leaf-drop to change into nutrient that goes back into the soil. There is nothing sinful about any of that! Consider too the droppings from animals eating grass and other plants - their dung has to be 'dealt with' naturally, so as to keep the biocycle going properly. As the plants are eaten, so they die, go through the alimentary canal and get dropped on to the soil. Plants were designed to be eaten as food for animals and humans. They died, giving strength to the creatures that ate them.

As for Satan being cast down to the earth; Jesus spoke of that thousands of years after Adam. The disciples reported demons fleeing at the name of Jesus, and he exclaimed: "I saw Satan fall like lightning from heaven." (Luke 10:17-18)

The trouble we have is that, for thousands of years, the creation has been subjected to futility (until a certain time when it will be restored). See Romans 8:19-23. But the way it was before Adam sinned was gloriously perfect. You are asking about a matter prior to Adam sinning, so there was nothing sinful about the biocycle then; the death of plants was a perfect system, and cultivating seeds of the field would play its part in feeding humanity, especially after they had been cast out of Eden.

is the biocycle (for example composting) death?

No. The bible makes a clear distinction between organisms containing "the breath of life" (reference), which many Christians believe excludes insects, which at least still take in oxygen. Accordingly, it should be clear that plants, which give off oxygen, are certainly not in the same category. (Similarly, bacteria and viruses are generally regarded as not "alive" in the Biblical sense.)

My assumption therefore would be that prior to sin, nothing died.

This is correct within the Biblical meaning of "life". Prior to sin, no vertebrates died (reference), and all animals were vegetarian (reference).

It makes me wonder why the need for Adam to cultivate

Nature, perhaps even pre-Fall, does not tend to be neat and orderly, whereas there are strong indications that God likes orderly. Perhaps, pre-Fall, plants would have naturally grown in the manner of a Japanese garden, with "organic" shapes, and various kinds of plants all mixed together, but I would suppose that something like a European formal garden would require Man's¹ intervention. Both can be beautiful. Both, perhaps, can supply adequate food. In that last sense, I suspect there was no "need" for cultivation.

However, Man was commanded to have "dominion" over Creation (Genesis 1:28). Creation was made for Mankind, with the intent that we would shape it to our usage and desires, carrying on in some sense the work of Creation which God started. Cultivating plants falls under this mandate.

(¹ Please note I intend this in the historic, gender-neutral sense.)

I am not a theistic evolutionist

Nor am I, in case the preceding references did not make that obvious. Theistic evolution is in blatant contradiction to Genesis 1-3, and indeed, to the very notion of the Fall. If there was death before Adam, nothing about Christian theology makes sense.

Fortunately, there is absolutely no reason to believe in theistic evolution. The available evidence strongly supports Creation and a Young Earth; it is only by excluding God a priori that other explanations of that evidence become necessary. Anyone that permits God to exist has absolutely no rational reason to believe in Evolutionism or Uniformitarianism. (That's not to say that Satan doesn't work very hard, and often successfully, to convince people to believe in these anti-Christian ideas anyway. "The lies of Satan are persuasive" is not a rational reason, however.)