As has been noted here many, many times, the AC booking site defaults to the lowest available fare class on a given flight, so you cannot specifically request and book H unless cheaper fare classes have been sold out. H fares generally must be booked through an AC res agent, or a TA.

As for the C class fare being cheaper than Y, that's not unusual on most routes where it is available. Y is fully flexible economy and thus the highest published economy fare, while C is a restricted business class fare and must be booked in advance and has more restrictions. Hence it is like a discounted, restricted economy fare which will be much cheaper than other fare classes.

This shows up on many NAmerican routes too where C is cheaper than Latitude Plus.