Wood is mostly cellulose (which is all carbon, hydrogen, and oxygen). There's some calcium and potassium, but not that much. You are correct that it's not entirely renewable.
Not sure what you mean by renewable? Would carbon, hydrogen and oxygen be more renewable than calcium and potassium? They are all just elements we have a lot of on earth.
And those elements don't get used up. Toss your wood on a compost pile, and you can re-use them?
Minerals follow cycles. If biological activity is utilising and removing specific minerals faster than they're returned to their respective sources (atmosphere, soil, or water, generally), then those minerals are depleted.
Leibig's Law of the Minimum states that it is the specific nutrient which is limiting of growth or metabolism which is most crucial. This is a point missed in numerous dicussions of growth or limits. Typically this is a fairly major nutrient such as nitrogen (fixed from the atmosphere, but at high metabolic cost, largely through microbes which are sybmiotes with legumes). Phosphorus and potash are the other most heavily utilised, and most frequently limiting nutrients. In parts of Australia, a land that is remarkably inactive, tectonically, critical micronutrients arrive as wind-blown dust, much from India or volcanic eruptions in Indonesia. A few grams per hectare can make a significant difference in crop yields.
Soil alkalinity is another major factor, as is drainage charcteristics, with sandy, clay, or high-carbon soils all being favoured or unsuited to specific plants. Then of course, climate, temperature, and precipitation.
Yes, minerals follow cycles. But so does hydrogen, nitrogen and carbon and oxygen. It's just that some of those are delivered via air, and some via liquids and some via the soil.
Nitrogen is an example of a nutrient which is present in air, but which is available through soil for the majority of all plants.
Again: nitrogen fixation is exceedingly energy intensive, and few organisms can achieve this on their own.
Where nitrogen is removed from soil faster than it is replenished, it becomes a critical, growth-determining, nutrient.
Carbon is available in the air, but also comprises a major constituent of topsoils. Though soil carbon itself isn't a plant nutrient, it provides a vital role in supporting plant life in its role in supporting symbiotic life, in managing alkalinity, and in moderating water and nutrient flows.
In many agricultural areas, soil carbon is being depleted at roughly 10x the rate at which it is formed, leading some to term such farming as "topsoil mining". Accumulations over a period of 10,000 years (since the previous ice age) are being degraded over a period of centuries.
Presence in the atmosphere != availability from the atmosphere.
But they are allmost unlimited in the ground. A intact forest, with deep roots in symbiosis with lots of fungi and other microorganisms retrieves them and make them avaiable to the rest of the forest via leave fall.
So taking out some trees at a time is sustainable. Chopping down all of them, is not.
Phosphorus would be better example. Even if you take only part of organic matter away, as long as it's faster than phosphorus availability from rock weathering, there's going to be a reckoning eventually.
Sure it can be added via fertilizer...if we'll be able to source such a quantity. It's not very abundant.