How does the order of place and subject affect the meaning of a sentence using the verb iru

Question

Consider the two sentences:

1. うちに犬がいます。
   uchi-ni inu-ga imasu
2. 犬がうちにいます。
   inu-ga uchi-ni imasu

Is it correct to translate these as

1. "There is a dog at home"
2. "The dog is at home"

respectively?

To me, the first sentence feels like a statement of fact, and the second feels like an answer to the question "Where is the dog?". Is this interpretation correct? If not, how does the order of subject and place affect the meaning?

Furthermore, how do either of these differ from the following sentence?

3. 犬はうちにです。
   inu-wa uchi-ni desu

Answer 1

uchi-ni inu-ga imasu (家に犬がいます) and inu-ga uchi-ni imasu (犬が家にいます) sounds, to me at least, the same. It's very commonly the case in Japanese that you can rearrange words and construct virtually the same sentence. Personally, I would say "uchi ni inu ga imasu". They both seem like statements of facts. If you were asked directly, "Where is the dog?" (犬はどこ？) you would probably just say　"uchi ni imasu (家にいます)" and omit the subject, dog, completely because it's obvious from the context.

There is a difference between inu-wa uchi-ni desu (犬は家にです) and the the other two sentences, however. You don't actually need ni before desu. ni arimasu and ni imasu can be abbreviated to just desu. For example "uchi ni imasu (家にいます)" is the same as "uchi desu (家です)." However, when you're using this form it sounds more to me like, "The dog is home" as opposed to the statement of fact that "the dog resides in the house." Nevertheless, depending on the context, in this case if you were asked directly, "Where is the dog?" they would both sound the same to me.