Yes, though it is closer in meaning and use to this. (that often corresponds to das / der / die and in writing to the otherwise old-fashioned jenes.)
Probably bad English, but i would say "what are you giving to the dog" or "what are you giving to that dog". I wouldnt use "this" unless i am showing/holding someone the dog.
I have to agree with James-I would only use 'that' in this sentence. So could this sentence also be translated as 'to that dog' or would that use a different word than 'diesem'?
But wouldn't dem Hund be just [to] the dog?
No. der, die, das (in any of their forms) mean both "the" or "that", and are often also used for "this".
English split up that word into two separate words "the" (originally from the masculine form) and "that" (originally from the neuter form), but in German, the same word still has both meanings.
"What are you giving this dog?" is grammatically correct and means the same as "What are you giving to this dog?" Can you please add it as an acceptable answer?
You have to apply the Perfekt or Präteritum tenses. It depends on the situation. I could be wrong though.