Sure "dat' sa" is what you say, I could figure it out on my own earlier, but I thought that there was the same phenomenon, because the object is a sort of subject, so here there is also a sort of passive logics.
In my sentence, "vitamíny" is in plural and "dat'" is, too. I thought that it was not a pure coincident. I guess that if vitamín was in singular then "dali" would change to "dal", that is "nedal by sa vitamín zo....".
Am I not right?
You're right to say that if we changed "vitamíny" to "vitamín," "nedali" would change to "nedal," as far as the grammar goes, and that's a good thing.
As for your other point, here's why I think it's not the same phenomenon:
nezvratné slovesá (non-reflexive verbs) - example: nakresliť (to draw something - e.g. a picture)
zvratné slovesá (reflexive verbs)(verbs with either sa or
si) - example:
nakresliť sa (to draw a portrait/etc. of oneself)
zvratné tvary nezvratných slovies (reflexive forms of non-reflexive verbs)(non-reflexive verbs with
sa only that look like reflexive verbs but retain their
non-reflexive meaning and are presented in a quasi-passive form) - example: Obrázok
sa nakreslil ceruzkou. (The picture was drawn with a pencil.) --> as can be seen from the example, the
main verb is in its reflexive quasi-passive form but retains its non-reflexive meaning.
In your example (#8), the
main verb is "vložiť" and "dať sa" is a
modal verb (other modal verbs: môcť/chcieť/musieť. . . ).
„Pán učiteľ, nedali by sa vitamíny zo špenátu a mrkvy vložiť do cukríkov a čokolády?“
In its
modal form, "dať sa" does not express what was done/is (being) done/will be done but rather what can/could be done or what one hopes can/could be done (i.e. dať sa = je možné / možno).
Dá sa to ešte opraviť? (Can it still be fixed? / Is it still possible to fix it?) -
Nedá. (No, it cannot. / it is not.)
Dalo by sa to ešte opraviť? (Could it still be fixed? / Would it still be possible to fix it?) -
Nedalo. (No, it could not. / would not.)
iPhone-y sa nedajú opraviť keď sa pokazia. (iPhones cannot be fixed once they are broken. / It is not possible to fix iPhones once they are broken.).
Nedá sa to ešte opraviť? (Can it still be fixed? / Is it still possible to fix it?) -
Nedá. (No, it cannot. / it is not.)
Nedalo by sa to ešte opraviť? (Could it still be fixed? / Would it still be possible to fix it?) -
Nedalo. (No, it could not. / would not.)
PS: In the weekend I checked a few threads on mo^j/tvoj/jeho/jej vs svoj, not just in Slovak, but also as regards Serbo-Croatian languague, and not just here in wordreference.com.
What seemed to be sure for me is that each time when there is a possibility of ambiguity, you have to use svoj. On the other hand the chance of ambiguity is much lower in case of mo^j/tvoj than in case of jeho/jej.
Some people says that you always have to abandon mo^j/tvoj if svoj works there, even if there is a possibility of ambiguity, some say, as you morior_invictus, that in this case one can choose either mo^j/tvoj or svoj.
We are already straying too far from the main topic of this thread but to answer your implied dilemma, Panceltic's
svoj is the only grammatically correct option in your case because the possessive pronoun you used indicated that the book belongs to the
subject of the sentence (i.e. you). If it did not, you would need to use one of the following:
môj, tvoj, jeho, jej, náš, váš, ich (
môj, in your case). Having said that, the grammatically incorrect use of
môj, tvoj, jeho, jej, náš, váš, ich in such cases is so common (and perhaps even preferred by some) that both versions sound fine to me.
Požičal si odo mňa svoje auto.

(the subject is
he whereas the pronoun intended is
my and thus, since the car does not belong to the subject of the sentence but to the person from whom the subject borrowed it,
svoje is not only grammatically but also semantically wrong as it would indicate that the car is his)
Požičal si odo mňa moje auto.

(for the reason stated above,
moje is the only option here).
Ten výraz som našiel vo svojom slovníku. 

(the subject of the sentence is
I and since the dictionary belongs to the subject of the sentence -
me,
svoje should be used in order for the sentence to be grammatically correct and to adhere to the general rule)
Ten výraz som našiel v mojom slovníku. 

(this sounds still fine to me even though Slovak teachers and linguists would probably frown upon it)