Yes, the same room type is available for all the 5 nights, standard award. I don't think it would let me book that room type for the 5-night stay otherwise.
And yes, the pricing does change if I book for more than one night, and not for the better. I checked booking a stay for nights 1-2 and nights 2-3. In each case Hilton wanted 38k. But night 2 by itself is 16k, so either of those combinations booked as single nights would only cost 19k + 16k = 35k.

Using the example in the FAQ, my total cost before discount is 92k, or 18.4k per night. Supposedly the rounding should benefit the member, so they'd count it as 19k. 92k-19k is 73k, not 75k. Even if the rounding doesn't benefit me and they count the average price as 18k, the total should have been 74k, not 75k. I hope someone from Hilton can explain all of that.