Maybe just some hints....... dont have time for details

Q1: Buy call short put,  short stock and take risk free loan at t and you should be able to make a arbitrage profit of eps
Q3: Write first w(t(i+1)) as w(t(i)) + (w(t(i+1)) - w(t(i)) )
Q2: use Q3's result and expand (Q(t) - T)^2
Q4: Yes, because Y(t) Should have 0 drift and be a martingale
Q5: Price should be just P*Prob(S(T)>K) = P*N(d1)
Q6: Apply Ito's lemma twice should do the job.....