G and K are produced from the same place in the mouth; they are just voiced/unvoiced versions of the velar plosives /g/ and /k/. When ㄱ is initial in Korean, it is unvoiced, i.e. /k/ (not /kʰ/). J is pronounced /tɕ~dʑ/ in Korean, whereas Z is pronounced /z/; these are both produced from roughly the same place in the mouth (the difference being that Korean adds a dental or alveolar stop in front of it. In loanwords, such as ‘zombie’, the hangeulisation is realised as 줌비; that is, Z is realised as ㅈ. The final -u in the Japanese word, is to the best of my knowledge usually mute. This means you get the following differences in pronunciation (IPA in brackets provided for Korean): Korean: ka-dzhok /kɐd͡ʑok/. Japanese: ka-zok
As you can see, they are quite similar, and (without actually having done an etymological control) in all likelyhood etymologically from the same word.
because the ㄷ has a sound more like a t when it's at the beginning of the syllable, just like ㄱ sounds like k sometimes