My Calamondins started putting out new growth about in the middle of August. And some leaves are halfway mature now, and so these days I find more and more newest branches fallen off the tree, on the substrate:

Is that likely? Because the previous time the similar thing was happening. Is this how a growth flush ends? The tree decides that it simply can't mature more leaves and drops the leftovers?

Oh! And also, if a tree is putting out new leaves does that mean the newly beared fruit will be growing more slowly? Cos now there's one fruit that's very small, from what I can remember fruit on my previous citruses at the beginning were growing pretty rapidly...

I'm not sure what's going on here, but no, it is not "normal" for a tree to drop young leaves or twigs. Flowers and young fruit, yes, you'll see quite a lot of dropping. But not leaves. Sorry to say, though, that I don't have any good ideas, from the photo, as to why this is happening with your plant.

the picture shows the roots--which are exposed and dry--a picture of the leaves might help.

That doesn't look to be a very healthy soil and root situation. At least from the picture. It looks like the outer medium is wet and the root area is dry. Are those rocks?

From what I know - that's how you're supposed to pot containerized citrus plants - leaving the top part of the roots exposed. I choose to believe that.

No, there are no rocks there. The mix contains 1:1 pine bark:peat moos.

Your right in leaving the TOP of the roots free,but your halve rootbal is exposed here !!
I don,t think that,s the right way,your roots are drying up,and the plant will die.

You just don't want to cover the trunk to prevent disease, so leaving a little of the first roots exposed helps prevent this. You should cover up most of what is showing.

It it were my tree I would repot it, trim some of the dead roots and redo your mix to at least 2:1 bark/peat. I think 1:1 is will hold way too much water. So, in your case some of your roots are drying out and others may be staying too wet. That's just my opinion.

+ repotting in September is not such a great idea and also when the trees are putting out new growth. I don't know how it is in the rest of the world, but the days are getting shorter and shorter in Lithuania and outside temperatures are dropping quickly, so most plants soon will go to dormancy, and despite that my citruses are inside they're no exception.

While it's true that you have more roots exposed than I'd normally recommend (I agree with the posters above -- I like to see a root or two, at the point they join the trunk), I have seen trees here with at least as much root exposure as you have, that were entirely healthy and happy, so long as the lower, buried roots were kept adequately moist. And if lack of water to the top were the problem, I'd expect the new growth to wilt and shrivel, but still not to fall to the ground as you're seeing. So I have to doubt that that's the problem. You don't have some sort of stem-cutting insect do you? We have sawflies here, that do that to roses, although I've never seen them on a citrus tree.

The new growth is actually wilting sometimes.

Much of the exposed roots are not the feeder roots, that absorb almost the entirety of the trees water. The roots that are showing (and I agree to much of the root system is uncovered) are the larger woody roots, which can easily survive under their present situation. I would agree with MarkT that a 50 percent peat moss medium is a bit much. 50 percent peat moss mixes have a tendency to compact quite a bit.. - Millet (855-)

So, I covered the roots, but what about fruit growth speed?
"And also, if a tree is putting out new leaves does that mean the newly borne fruit will be growing more slowly? Cos now there's one fruit that's very small, from what I can remember fruit on my previous citruses at the beginning were growing pretty rapidly..."
???

Certainly the rate of fruit growth varies throughout the seasin, as well as with temperature. But I don't believe it is associated directly with the presence/absence of a vegetative growth flush.

This fruit has been this big for a few weeks now:

From what I can remember when growing Calamondins earlier the fruit were getting bigger by the day at such early phase.
Is this related to the fact that it's Fall right now?

I just checked a lithuanian citrus forum and someone's fruit on a Citrus limon from bloom to an egg sized lemon took about 1.5 month to grow.