1. Yes, 입니다 is the polite form of 이다 :) They usually follow the noun like 여자이다. 2.습니다 is the polite form of verbs and adjectives. 먹다(eat) ->저는 사과를 먹습니다 했다(did) ->저는 공부를 했습니다 귀엽다(cute)-> 강아지는 귀엽습니다 If there's the final consonant in the syllable before '다', like '먹다(먹)', you just remove '다' and put '습니다' to make it a polite form. And if there's no final consonant in the syllable before '다', like '하다(하)', you remove '다' and put the final consonant 'ㅂ' and '니다' next to it -> 하+ㅂ니다 =합니다. Ex) 가다 -> 가+ㅂ니다 =갑니다 갔다-> 갔+습니다=갔습니다 예쁘다-> 예쁘+ㅂ니다=예쁩니다 행복하다-> 행복하+ㅂ니다=행복합니다 I hope this could help you :)

There are seven speech levels in Korean. -ㅂ니다 and -습니다 are the ending suffix of Hasipsio-che -ㅂ니다 is used after a verb or adjective which ends with vowel or ㄹ -습니다 is used after a verb or adjective which ends with consonant except ㄹ -다 is the ending suffix of Haera-che -(어/아/여)요 and -에요 are the ending suffix Haeyo-che -어요 is used after a verb or adjective of which final vowel is ㅓ, ㅕ, ㅜ, ㅡ, ㅣ, ㅐ, ㅔ, ㅖ, ㅞ, ㅚ, ㅟ, ㅢ -아요 is used after a verb or adjective of which final vowel is ㅏ, ㅑ, ㅗ, ㅘ -여요 is used after 하다 verb -에요 is used after 이다 or 아니다 Hasipsio-che(Formality: high, Politeness: high) is a common style of speaking. A conversation with a stranger will generally start out in this style and gradually fade into more and more frequent haeyo-che. It is used between strangers at the start of a conversation among male co-workers by TV announcers to customers Haeyo-che(Formality: low, Politeness :high) is remarkable in that it is used both with higher level pronouns (namely, titles) as well as the middle level second person pronoun dangsin. It is used mainly: In Korean phrasebooks for foreigners. Between strangers, especially those older or of equal age. Between female co-workers or friends. Haera-che(Formality: high, Politeness :low) is generally called the "plain" style. It is used: To close friends or relatives of similar age, and by adults to children. In impersonal writing (books, newspapers, and magazines) and indirect quotations ("She said that..."). In grammar books, to give examples. For example with 여자이다, 나는 여자이다 is Haera-che 저는 여자에요 is Haeyo-che 저는 여자입니다 is Hasipsio-che with 크다 집이 크다 is Haera-che 집이 커요 is Haeyo-che 집이 큽니다 is Hasipsio-che with 작다 집이 작다 is Haera-che 집이 작아요 is Haeyo-che 집이 작습니다 is Hasipsio-che with 먹었다 사과를 먹었다 is Haera-che 사과를 먹었어요 is Haeyo-che 사과를 먹었습니다 is Hasipsio-che Refer to https://en.wikipedia.org/wiki/Korean_speech_levels