-(ㄹ)거라 is a contraction of -것이라. 거라 and 것이라 are shortened forms of -것이라고 which means "that ..." (quoting). 그녀는 다 잘 될 거라 말했다 = .. 거라고 말했다 = .. 것이라고 말했다. => She said it will all turn out alright. 거리 is just a noun with a few different meanings. 1. street boulevard 거리의 불빛: lights on the boulevards 2. distance 서울과 부산 사이의 거리: distance between Seoul and Busan 3. stuff, material (for some purpose) 놀 거리: things to play with, 일거리: job, work (to do)

By the way if your Korean is anywhere near intermediate level, you might check this. It's a couple lines from a fine song called 시간이 흐른 뒤에 ("With The Passing of Time" - https://www.youtube.com/watch?v=D-zBGTb2vUI). It has "거라" (and "거야" which is related) exactly in the sense of the above explanation. 잊을 수 있을 거라 나는 생각했어, 시간이 흐르면 몰랐던 거야 갈수록 더해가는 아픔을 It would all be forgotten, I thought to myself, with the passing of time I had no idea that the pain was only to get worse