The transliteration of the sentence is "He of three daughters are" without the "hain" verb ending there would be no sentence. It would be a meaningless phrase like "three daughters of he" with the translation "his three daughters". When you add the "hain" at the end you are saying that those three daughters exist and then we translate it to "He has three daughters."
There is no proper "to have" verb in hindi... I got that confirmation by a native speaker. Either it is "with me" (ke pas) or that hai/hain at the end of the sentence to say that the person exist in relation with the subject (that is my personal understanding, I don't have my native speaker handy right now). Moreover, yes uski should be translated as his or her (he/she has) and both should be accepted as an answer...
रखना meens keep/have/put, according to wiktionary. के पास is used to show ownership, but is not a verb. I remember using this phrase in India to ask for a ciggy. Would like to have an Indian's opinion. This has been asked several times in this discussion, but no answer. Perhaps a later Hindi lesson here will help us with this though.