Your interpretation of using “des” seems correct; it would seem a shortened way of saying “J’aime quelques-uns des livres qui contiennent des dessins.” But with “les”, the whole phrase becomes the object of “aime”. So to say that you like all the books which contain drawings, “J’aime les livres qui contiennent des dessins.” is the way to go.

I

J’aime les livres qui contiennent des dessins.

This specifies all books that have drawings in them; it is a generic reference to “book that has drawings in it”. The article “les” (as in English “the” (singular noun), although “zero article + plural noun” is used much more often) is used to speak about species, kinds of things, etc. When you say that then you are saying that you are sure to like any book containing drawings and you could say it that way too;

J’aime n’importe quel livre qui contient des dessins. (“n’importe quel” is “any”) or
J’aime tout livre qui contient des dessins. or
J’aime tous les livres qui contiennent des dessins. (same thing for the three sentences, but you insist on the fact you like them all)

II Yes, in this grammatical context “des” is “some”.

J’aimes des livres qui contiennent des dessins. translation: “I like some books that contain drawings.” (“des” is “some”)

In this sentence you use the indefinite article “des”; it’s the plural of “un”. So in the singular you’d have to say this;

J’aime un livre qui contient des dessins. translation: “I like a book that contains drawings.”

It means that you know a book, may be you don’t own it (it’s in the library or it’s your friend’s book) but whatever the book, you like it. If you use the plural, it’s the same thing: there is a group of books and you know all of them and you like all of them. You didn’t use a generic reference in this case and that means that you don’t necessarily like all the books that exist which have drawings in them.