Here are grammar point answers to your questions. 1) 그냥 보고 싶어서 = Just because I wanted to see you. Yes, 어서 indicates reason (i.e. it indicates the reason for something said just before this sentence). "I just want to see you" would be 그냥 보고 싶어. 2) 지금 데이트 신청하는 거야? 거야 and its full form 것이야 mean "it is the thing/point" (것 = thing, matter, point, "that"), and has no sense of tense. The tense is determined by verb forms. For the future tense, a particular verb form is used with 것이다., - 나는 노력할 것이다 ("I will try" - future). The -ㄹ verb ending indicates what's to come or an open possibility, like the infinitive in English. You combine the-ㄹ form with 것이다 to get the future tense: X-할(to do) + 것이다 (it is that) = It is that I am to do X = I will do X. Compare it with other similar structures - in all these 것이다 forms an indirect sentence, like an observation. - 노력하는 것이다 (present). (The fact of the matter is that) I am trying. - 노력한 것이다 (past). (The fact is that) I have tried. - 노력했던 것이다 (further past). (The fact is that) I had tried. 3) 그래. 좋아. 몇 시에 볼까? 그래 is short for 그러해, a variant of 그러하다 or 그렇다 which means "It is so"; or it can be 그리해 or 그렇게 해, meaning "(go ahead and) do so". In both cases, it implies "Yes", as in "Yes, it is" or "Yes, (please) do so)". 볼 in 볼까? is from 보다. It's in the -ㄹ form mentioned in #2 followed by the question suffix 까. -ㄹ까? is a common question ending asking whether someone agrees to what you're suggesting to do (우리 이제 갈까?), or asking about a possible outcome of something (내일 비가 올까?).

1 I just want to see you 2 Are you asking me out right now? Or Are you asking me out on a date? 3 Yeah, sure, when do you want to meet?