In the second example conversation the first two lines read:
I have learned that if the subject is not mentioned in the sentence, then it is implied from a previous sentence or simply out of context. For example, if I was in a conversation about going to the store, I could say:
I didn't have to say "わたしは" the second time because it is understood that I am speaking of myself. However, in the two lines listed above from the example conversation, in the second line が is used instead of what I would think should be は. Using が would lead me to believe the subject is still person B when in fact is has changed to "this dog" (このいぬ). That being said, the sentence could be translated as "I am this cute dog." or something to that effect could it not? So I'm thinking it would be:
The difference between WA and GA is such a complicated topic. You need to read a whole book to understand it fully. But, of course, you don't have to do that unless you are planning to become a linguist. The basic rules are:
GA is a subject marker. WA is a topic marker. (The word that is marked by WA ( = topic of the sentence) can be a subject as well, but not necessarily so.)
In this situation, the example sentences are right. The person A asks the person B which dog he likes among all the dogs there are in front of them. And the person B picks one that he likes and says, "This one is cute." The both subjects (DONO INU and KONO INU) are marked by GA, and there is no hidden subject, "I", as you suspected:
A: どのいぬが すきですか。 (DONO INU GA SUKI DESU KA?= Which dog do you like?) B: このいぬが かわいいです。 (KONO INU GA KAWAII DESU = This dog is cute.)
Your suggested sentence, このいぬは かわいいです(KONO INU WA KAWAII DESU), sounds like "This dog is cute, but other ones are not (in his opinion)". The usage of GA for the position where WA normally goes usually means "comparison" or "emphasis". In this sentence, the subject implies that THIS dog (compared to others) is cute.
GA & WA Thank-you for helping me with this insanely complicated GA and WA business. I have noticed in several places the comment "you could read a whole book on GA and WA" so now I am curious; is there such a book? If so, could you please tell me of it? I do have some interest in one day doing translations and interpretations so I am interested in such a book... even if it won't do me any good for a while.