For me, they are the same, much as "He started to study" and "He started studying".
(But "He stopped to study" and "He stopped studying" are different! -- Here, only "He stopped studying" means "Ders çalışmayı bitirdi" while "He stopped to study" is "Ders çalışmak için durdu".)
He started to study = He started studying = Er fing an zu lernen
He stopped studying = Er hörte auf zu lernen
He stopped to study = Er hielt an um zu lernen
As for Sen dersi çalışmak seviyor musun, Alex said above that sevmek needs the accusative case, i.e. çalışmayı seviyor rather than çalışmak seviyor.
And as for ders çalışmak versus dersi çalışmak, I can't say. But I imagine one (with accusative dersi) would be "study the lesson" and the other would be more general, "study lessons in general, study".
What is the difference between ders çalışmak, öğrenmek and okumak(when it is used as to sudy), please?
My dictionary translates them in a very similar way, so it seems they are interchangeable, but I feel like that is not the case at all. I thought öğrenmek means to learn something, as in I am learning Turkish = Türkçe ögreniyorum. From what I gather, ders çalışmak cannot be followed by an object, so it can only refer to the activity of studying. I am not quite sure about okumak. The dictionary says it is used in sentences such as I study at University.
But I am still confused about the use of these verbs. I would be very grateful if you shed some light on how to use them :)
In my opinion: yes.
You can "study for a lesson" - that would imply reading through your books and your notes in order to understand the material ("study") in preparation for a lecture the next day (the "lesson").
You could probably also "study a lesson", which for me would imply reading through that part of a book corresponding either to a lecture that you had, or one that forms a particular unit of the book ("Lesson 5: Stars and Planets", that sort of thing) even if it is not connected to a physical class you attended, perhaps because you are learning a topic by yourself from books and are dividing up the time into your own lesson-sized blocks.
But "I will study lesson" just sounds wrong to me.
A few more such verbs:
I forgot calling you. = seni aradığımı unuttum. (aradım; ama o ânı hatırlayamıyorum.)
I forgot to call you. = seni aramayı unuttum. (Seni hiç aramadım.)
I regret to inform you. = Size bildirmekten üzüntü duyuyorum.
I regret informing you. = Size bildirdiğime pişmanım.
I tried doing it. = Yapmayı (şöyle bir) denedim.
I tried to do it. = Yapmaya uğraştım.
It means hurting people. = İnsanların incinmesi anlamına geliyor.
It means to hurt people. = İnsanları incitme niyetinde. ('It' derken kastedilen şey neyse artık.)
I understand that the context is important for the one or the other, but I not yet got it completely.(I mean what Ektorasan was writing) It would have been helpfull for me to get an English explanation for the different sentences.
It is fully clear to me what Miziamo is writing, but here is remaining the Turkish translation of it to bring light in my dark tunnel
Because the subject of çalışmak and sevmek are the same. It's you who studies, and it's you who loves it. In this case, saying çalışmaNı would make the sentence too heavy. If the subjects were different, then by all means go ahead and use it: Ben ders çalışmaNı seviyorum. (I like your studying / I like how you study.)