Iginla2010

25.4  if we increase the frequency with which we observe the asset price, it would be less possible to hit the barrier price. this is to say the price of down-and-out call would be more valuable and down-and-in call less valuable.
25.5  There would be 2 cases in this question, either the asset price hit the barrier price or not. For the case barrier price being hitted, Cdi=C, Cdo=0. while for the other case that barrier price not being hitted Cdi=0, Cdo=C. therefore, no mater in which case, the Cdi+Cdo=C.
regarding to the other questions, i have no idea as well.