I forgot about the 봐. ^^;; There are a lot of usages for 봐 but with your example "다가와봐", it means "Come to me." 다가오다 means to approach or come, and the 봐 here means "to me". So it makes sense if it is said twice. XD

I will use the verb, 오다 (to come), to explain. When Koreans ask you to do something, they will often ask you indirectly. One of their ways to ask indirectly is to use "Try to~." So, instead of saying "Come," they'd say "Try to come." 와요 (come). ~보다 (to try to~) 와요 + 보다 becomes 와보다. The command form of 보다 is 봐. So Try to come is 와봐. i.e. Try to go (가요+ 봐) = 가봐. Try to eat (먹어요 + 봐) = 먹어봐. Try to smile (웃어요+ 봐) = 웃어봐. Try to do it (해요 + 봐) = 해봐. Try to come closer / approach (다가와요 + 봐) = 다가와봐. 다가와봐봐 is a colloquial expression, and is the same as 다가와봐. i.e. 먹어봐봐 = 먹어봐, 해봐봐 = 해봐, etc. The similar expression of 와봐봐 in English might be "Cooome!" i.e. 와봐봐: Cooome. 이리 와봐봐 = 여기 와봐봐: Come heeere.

-와 and -과 is a conjunction which connects noun + noun, or noun phrase + noun phrase. They both mean "and". Sometimes it can also mean "with" but they are often seen in written language and not common with speaking form. It is more common to hear people use -(이)랑 when speaking to another. Examples: 오늘은 친구와 영화 보러 갈 거예요. (Today I am going to see a movie with my friend.) 저는 연필과 지우개가 필요해요. (I need a pencil and an eraser.)