The rule you stated makes it appear like any verb stem ending with a syllable containing ㅗ will make the verb conjugate with 와(오 + 아), but that's not the whole story, as there are exceptions. It is because ㅂ is phonetically close to 우 and thus normally likes to go with 어, so that only a strong ㅗ in the stem ending can overcome this innate 우 preference. For 새롭다, although 롭 has ㅗ in it, it is not strong enough because it's a suffix rather than a proper part of the stem. -롭다 appears in adjectives like 이롭다, 해롭다, 새롭다, 여유롭다, 상서롭다, and others as a suffix. So I think the best way to deal with it is to remember the two exceptional cases (as far as I know) of 돕다 and 곱다 that go with 와, and use 워 for all others. Note however that there are two different adjectives spelled 곱다, of which only one is irregular. - 돕다 (to help) -> 도와주세요. - 곱다 (smooth and fine-grained, fair-skinned. ㅂ-irregular adjective) -> 얼굴이 고와요. - 곱다 (numb from cold. regular adjective) -> 손이 곱아요. This shows that you can't always go by the grammar rules when dealing with irregular conjugations. Often, you just have to memorize the special cases because the exceptions don't follow any logic or rule.

새로워 is correct spelling. 새롭다 is a ㅂ irregular verb. According to vowel harmony rule, 새로와 is correct. But most Korean people say 새로워 instead of 새로와 for easy pronunciation. So 새로워 was accepted as a correct spelling. ㅂirregular verb/adjective rule is: When a word stem with final consonant ㅂ + a particle start with vowel, ㅂ changed 우 or 오. * ㅂ => 오 (only before 아 vowel) => 와 There are only two verb/adjective 돕다(help), 곱다(beautiful) in this category. 돕(다) + 아요 => 도와요 곱(다) + 아요 => 고와요 돕(다) + 으면 => 도우면 곱(다) + 으면 => 고우면 * ㅂ => 우 어렵다, 쉽다, 덥다, 춥다, 귀엽다, 밉다, 아름답다, 맵다, 눕다, 줍다,반갑다,사납다, 가볍다, 무겁다.... 덥(다) + 어요 => 더워요 반갑(다) + 어요 => 반가워요 덥(다) + 으면 => 더우면 반갑(다) + 으면 => 반가우면 NB. 입다, 잡다, 씹다, 좁다, 넓다, 뽑다, 접다 are not ㅂirregular verb/adjective