To clarify Olimo's correct, but not necessarily helpful if you don't already know it, answer: for living beings in plural, the accusative takes its form from the genitive (also in singular for masculines). So собак is both the genitive and accusative plural of собака. As he says, it's acting as an accusative here.
I don't know how to differentiate between "What are the dogs eating" and "What do dogs eat". They are both correct but I feel like they convey slightly different messages. Is there a way to say "What are the dogs eating" another way in Russian? Maybe "что собаки едят?"
As Russian verbs have no continous/progressive aspect, we can only render this difference by adding some words, e.g. What are the dogs eating? - Что собаки едят сейчас? / Что едят собаки сейчас?/Что едят собаки в данную минуту?/ Что едят собаки, пока мы с вами разговариваем? Otherwise, sentences can be understood both ways, regardless of the word order
Absolutely. Different contexts, though, require different intonations. Three scenarios are possible. (1) To the question “Do you know what dogs/the dogs eat / are eating?” (Знаешь/Знаете, ЧТО собаки едят?) we respond by asking, ЧТО собаки едят?/ЧТО едят собаки?/ЧТО же они едят? (“What do they eat?/What are they eating?”) (2) The questions «Что СОБАКИ едят?» and «Что едят СОБАКИ?» both mean “How about [the] dogs, what do THEY eat?” Finally, (3) the questions «Что ЕДЯТ собаки?» and «Что собаки ЕДЯТ?» both mean “What do the dogs EAT?”, implying that the asker already knows about other needs or habits of the particular dogs.