Let's pretend there is no end of the world, and the world lives eternally. Can we ever run out of elements?

I tend to consider the world to be composed of the elements, so by definition, eternal world=eternal elements.

It is possible that chemical processes could proceed in such a way that the specific compounds now present would be replaced by other compounds. The elements would remain. their availability for specific ends could be eliminated or severely reduced.

For example, there is a huge amount of oxygen in rock. We can't use that oxygen to live. The existence of that oxygen is not useful for our needs. It is likely that the free O2 that we now rely upon will eventually get sequestered (removed from air and stored somewhere) into unusable forms over time. The only reason it is present now is because it is produced by plants at about the same rate that it gets removed by animals and inorganic chemical reactions. Stop the production by plants, and O2 will disappear, and us along with it. But the oxygen will remain. It simply would not be as O2.

<and there is nothing that creates elements> Obviously there is, or no elements would exist. We know that all elements heavier than helium, what astronomers call metals, are synthesized in supernovae. And humans are capable of creating elements that don't even exist in nature, not in great abundance and not without starting with other elements to begin with, but there are two things that create elements right off the bat.
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<Like, in trillions, gazillions, blushtaimalimillions of years, would there ever be a time when earth runs out of elements in the air?> In around a billion years Earth will be uninhabitable as the Sun begins to heat up, so let's limit the question to that. Are you asking if we could deplete oxygen from the atmosphere? It's not impossible, and that's pretty much the only thing in air we'd worry about depleting. Everything else is pretty much either nitrogen, which we don't need to breath, or contaminants that we'd rather not have in it. There are useful gases like argon that are fairly easily obtained from air, but it's a noble gas and so isn't used up in any way, just endlessly recycled. And as far as oxygen goes, well, if we used it all up, that would pretty much be a self-limiting behavior, wouldn't it?
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The bottom line is that if we still exist a million years from now, never mind a billion or a trillion or a blushtaimalimillion, we will either have learned to live within the limits of what the planet gives us, or we will have moved far beyond it. If we ever get to the point of building Dyson spheres or ringworlds we might have to worry about the material limitations of the Solar System, but by then we'll probably be inhabiting other solar systems and the point will be moot.
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I dont understand your question

No - where would they go? As for "nothing creates elements" that is not precisely true either.