1. 이쪽으로 오세요 => Come this way, please. (이=this, 쪽=side, direction).
으로 is a particle with many uses, but when connected with a location, it means "to" or "toward" that place.
2. 물론이죠 => Yes, of course.
3. 저쪽에서요 => On that side. In that place. Over there. (저=that, 쪽=side, direction)
에서 is like "in/from (a place)", the opposite of 으로. It indicate the place where something happens.
저쪽 usually indicates a place the two people can see but not close close by.
4. 어디서 입어 봐요? (= 어디에서 입어 봐요?) => Where can I try it on?
"서" is a contraction of "에서"(as in #3 above) which happens after vowel-ending syllable.
입어 보다 = 입다(put clothes on) + -아/어 보다 (try something as a test/trial) => try it on to see if it fits.
You can answer this question with 저쪽에서요, 저기 보이는 탈의실에서요 (In that dressing room you see over there), etc.