-걸 is short for -것을. It usually emphasizes a feeling or thought one has, evoking a sense of stopping short as if to think about it. In writing, it's fairly similar to ending something with the ellipsis mark "..." or sometimes using the "when" clause. "꿈만 같은 걸" can be translated as "It's (just) like a dream" with an emphasis on "dream". 만 after 꿈 is almost like a set phrase rather than meaning anything specific. "It's only like a dream" is probably closer to 꿈같기만 한 걸. "왠지 맘에 드는 걸" is "For some reason I like it [you, something]", as you said. 걸로 알다 or 것으로 알다 corresponds to "take/understand as (something)". For example, - 연락 없으면 잘 도착한 걸로 알아 = If you don't hear from me, that means I have arrived without incident. - 그 말, 오케이한 걸로 알겠어 = I'll take your word as a yes. - 그가 미안해서 머뭇거린 것을 난 수긍한 걸로 알았던 것이다 = It so happened I mistook the sorry hesitation on his part for acquiescing tacitly.