'꼭' means 'surely', 'certainly' or 'exactly' '해줄테니까' is '해주다' and '~할테니까' are combined which mean 'do as a favor' or 'do for' and 'will be' or 'will do' '꼭 해줄테니까' means 'I'll do something for you at any cost' '못생기게' means 'ugly' '그릴 수도 있어' is '그리다' and ' ~할 수도 있어' are combined which mean 'draw' and 'may' '못생기게 그릴 수도 있어' means 'I can draw a picture but it may looks like a little ugly' '마음' means 'mind', 'heart' or 'feeling' '그게 아니야' means 'that is not' '마음은 그게 아니야' means 'that is not really mean it' or 'didn't mean it' I hope that is helpful to solve your problem

테니까 ex) 테니 테야 테다 '테' is abbreviation for '터이'. (ㅓ+ㅣ) And '터' of '터이' is bound noun. Eventually, these are all conjugated form of '터이다' '터' means 'be expected' or 'be supposed' or 'wil' '꼭' means 'surely' or 'certainly' or 'undoubtedly'. Use to sentence adverb.