Cumulus is absolutely right.

And your examples, Antonio, are right as well.

If there is a compound sentence like

Я видел девушку, которая читала книгу. - "девушка" is in accusative (green) since it is a direct object of the first clause, but "которая" is in nominative (red) since this word (которая) is a relative pronoun which serves as the subject of the second clause.

But when we use a participle

Я видел девушку, читающую книгу. - Both "девушка" and "читающая" are in accusative now, since there is no second clause! There is only one clause now, where "читающая" is an attribute of "девушка".

Compare:
Я видел красивую девушку (adjective).
Я видел читающую девушку (participle).
Я видел читающую книгу девушку (participle with a dependent word).
Я видел девушку, читающую книгу (more natural word order for a participle with a dependent word).

So, participles are very similar to adjectives in this regard. They are like "verbal adjectives".

Even in Greek in order the sentence to be meaningful I should use которые and not которых, because if I use которых then the sentence will be translated "This class includes: - activities of crediting instutions, of whom do not receive deposits" so the meaning totally changes.
Actually, in Russian it is the same. We also say "которая" and not "которую" in case of a compound sentence. You just selected a wrong example. It is about compound sentences and not participles. If you rephrase it with a participle, you will get: "activities of crediting institutions not receiving deposits" which is structured as "activities of (crediting institutions not receiving deposits)" where "of" is applied not just to "crediting institutions" but to the whole part in brackets. Maybe it is not a good English, but try putting it this way: "activities of not receiving deposits crediting institutions".