both 새 and 새로운 mean almost same, meaning of NEW. for ex, new book = 새책 or 새로운 책. 새 and 새로운 is adj., located in the front of Noun. But, exactly, this is a new phone = 이것은 새 전화기입니다.(I buy a new phone) or 이것은 새로운 전화시입니다(I buy a new phone (coz mine is too old) or I buy a up-to-date phone that is of recent invention.

that was really good without a doubt. 의심의 여지 없이 정말 잘 했어요. without a doubt, 의심 하나 없이~, 의심의 여지 없이, 의심 없이.. We can translate it widly.. But, it's better to translate liberally, "확실히"(surely)

blind=장님, 맹인, 시각장애인 But, as your translation, I can't see(저는 볼 수 없어요), it is also good expression.

~해야 합니다 ~할 필요가 있습니다

형제 = brothers 남매 = brothers and sisters 자매 = sisteres. Although you ask '형제' to boys, they would reply all their siblings, sisters and brothers. But, you should ask '형제' to only boys. Of course, you can ask '남매' too. If you want to ask it to girls, you should use the word "자매' or '남매".

the most, the best. In Korean, we have lots of expression up to the situation. But, your example can be translated to the below. The most good manner one.(The best manner one) 가장 좋은 매너를 가진 사람

in this sentence, you should pronunciate '오시예요'. When 받침 of words+'이'(only vowel), 받침 should be pronunciated with '이'. 옷+이예요 should be pronunciated to 오+ㅅ+이예요=오시예요. But, 받침 of words+'히'(it is not only vowel) doesn't link with next word '히'. for ex, 열심히, [열심히]

Yes, your understanding is right. ^^ 졸라=very much, kind of slang. use it with closed friend only. 득=advantage, profit..