Cure is the same or even a bit longer with HP since they tend to have more water. Most of my recipes cure for 6 weeks unless it's a salt bar (several months) or castille (1 year). I haven't played with liquid soap yet, but I think liquid is just used for different thing than bar soap... regardless of castille or not.
I'm a CP girl who only does HP when I'm dealing with a real ornery FO that doesn't take kindly to CP, or when I'm making hubby's shave soap which contains a lot of stearic acid (which also doesn't take kindly to CP).
Re: cure: The least amount of cure-time for me is 4 weeks for CP, but longer is always better, of course- especially for Castile's (anytime after 3 months cure is good enough for me with my Castile's). I like to cure my HP soaps a little longer than CP because of the excess water- probably 6 weeks at the least.
Re: Castile's: I've never made or used a 100% liquid Castile soap, but I do make a Castile-type liquid soap with 65% OO in it, which I like a lot for hand-washing at the sink. I don't like showering with liquid soap, by the way- I prefer bars in the shower. The bar-type of Castile is an acquired taste. People either love them or hate them. I only like using my bar Castile in the shower if I have a nylon pouf handy. If there's no pouf- I don't use the Castile. They have really slimy, snotty, sparse lather without a pouf. But with a pouf, the lather is awesome.
Another CP girl here. HP Shave Soap though. I too don't make castile anymore (I have some I made a long time ago). I prefer bastille. I too cure at least 4 weeks for CP but prefer 6-8. HP 6-8 weeks. Salt Bars 3 months or longer.