Translation:The dog stands.
to conjugate into a formal declarative sentence, the pattern is [adjective/verb stem + (스)ㅂ니다].
[A/V + ㅂ니다] if there's no batchim (ending consonant) or the A/V stem ends with a ㄹ.
[A/V + 습니다] if there's a batchim at the end of the A/V stem.
here, the verb is 서다, and its stem 서.
서 + ㅂ니다 = 섭니다
well you might have come across 재미있다 and 재미없다, meaning respectively "(to be) interesting, fun" and "(to be) uninteresting, dull". their non-past formal polite forms are 재미있습니다 and 재미없습니다, both following the 2nd pattern [stem + 습니다] because their stems have a final batchim.
most of the time they conjugate the same, however in the plain form adjectives conjugate differently. For example, 서다 in the plain present form is 선다. Whereas an adjective like 재미있다 stays the same in the plain present form with no changes. Another crucial difference is that adjectives cannot act on objects much like in English. Therefore you cannot use the object particle 를/을 in a sentence that ends in an adjective.
One reason you might get translations of both "The dog stands." and "The dog is standing." is that in real life, Koreans don't usually differentiate the two.
If my wife asks me "어디 가요?", she's asking me where I'm going and not "Where do you go?"
Similarly, "뭐 해요?" is usually said when they mean "What are you doing?" rather than "What do you do?"
I think you could use 개는 in this case, but: 이/가 is more like a subject marker where 는/은 is more like a topic marker.
The latter (는/은) is used more often for general statements/truths (or things asserted to be generally true). And 이/가 is used often for specific subjects.
Like if I say that water is blue, it could be "물은 파랗아요." But if I said "물이 갈색이에요.", it would mean "The water is brown."