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.