I am wondering why this sentence is so important - I seem to get it every day during my reviews and I answer correctly each time. (;-)
I think because in these sentences, the Duo Lingo designers are trying to reinforce in our minds the use of "szukać + genetive" and "pomagać + dative". Very tricky for me as an English speaker.
But is this translation correct? I thought it means "We help his grandpa", and that if we want to say "We are helping our grandpa" we should say "Pomagamy naszemu dziadkowi".
Any form of "swój" refers back to the subject of the sentence. The subject of this sentence is "We": We help. So if we help "swojemu" dziadkowi, that means we help our grandpa. If "Oni pomagają swojemu dziadkowi", then they help their grandpa. And so on, and so on.
"Pomagamy naszemu dziadkowi" is perfectly fine.
Basically, if you can use a form of "swój" correctly, do it. Some 'normal' forms (mój/twój/jego/wasz etc.) feel more natural than others in a sentence which could use 'swój'. So 3rd person possessives actually suggest that this "his/her/their" is different than the subject of the sentence. That Adam is cleaning John's car, not his own. 2nd person possessives used instead of "swój" seem very clumsy. But 1st person are actually pretty okay.
Is there a logical reason for why dziadka is Dative? More than just 'thats how it is'?
The basic, Nominative form is "dziadek".
Dative "dziadkowi" is used here, because the verb "pomagać" takes Dative. Why? It's easy, Dative is used for the indirect object of the sentence. Grandpa is the 'recipient' of the action of helping.
I am not (yet) very proficient at Polish, but I have studied German grammar at a reasonably high level at the university. I think this way of conceptualizing dative verbs may be confusing to learners. As far as I know all indirect objects require the dative in both German and Polish. This is the case after verbs like dawac/geben or opowiadac/erzählen, where the direct object is in the accusative and and the indirect object is in the dative. However, quite a few verbs require that the DIRECT object have the dative form. Interestingly, the most common verbs that this applies to are the same in both Polish and German: congratulate, help, fit, answer, thank and quite a few others. I may be mistaken here, but I don't think there are many (any?) schools of grammar that would say that the dative in this sentence is caused by the noun being the indirect object in this sentence. It is a direct object in the dative because the verb governs the dative.
Well, you could look at this sentence as "we are giving help (direct object) to our grandfather (indirect object)."
Incidentally, quite a few verbs take genitive., "potrzebować" being a case in point.