i) Why would you check a subgroup os associativity ? and why are you complicating the definition of associativity ? I learnt it as and a subgroup will trivially inherit the associatively property.
also (12) is short hand for (12)(3)(4).
for ii) there is no identity, so move on, don't bother checking for everything when one property clear fails.
iii) did you prove it was closed ?
iv) refer to i)