Now I can say that the two seeds I couldn’t identify so far are from the Medlar (Mespilus germanica) species.
And here’s how I found out:
First, I tried online plant identification via forms. Problem being that I didn’t know AT ALL what the leaves or flowers look like. So that didn’t get me anywhere.
Then I just googled “Turkish Fruit” and got a list of about 20. I knew most of them, so I only checked out the two I didn’t know how they looked like (the list had no pictures). This left me with either Medlar or Russian Olive, but I tended towards Medlar. Then I wrote to my friend who had been with me when I collected them. She said it was Medlar all right. (Actually, she said it was muşmula, because that is the Turkish name for it. And one cannot be expected to know all fruits’ names in English when one isn’t a native speaker.)
Medlar has quite the interesting cultural history. I don’t think it is common at all in Germany despite its Latin name. However, in Medieval and Victorian England, it was very popular. Both Chaucer and Shakespeare mentioned it in their work, according to Wikipedia.