1. I think drawing is fun.
→그림 그리는 건 재밌다고 봐.
'-ing' of English is similar to '-기' and '-ㄴ 것' of Korean. '그리는 건' is the shortened form of '그리는 것은' as an oral speech. 'I think' can be translated into '-다고 보다', '-다고 생각하다', '-ㄴ 것 같다', '-ㄴ 듯하다', etc.
2. I like going out and taking long walks.
→나는 밖에 나가 오래 걷는 걸 좋아한다.
One of ways conjugating as AND is by '-아/어' form of the verb in Korean. '나가다' with the form is '나가,' so you can use like that. 'taking long walks' can be changed '오래 걷는 것' as the first sentence. '걸' is the shortened form of '것을.'