The thing with H's 236A, is that although it's faster in every way, it can be CROUCHED under, making it really bad in pressure strings. :\
You could use 236B instead which isn't as punishable but relatively safe.
I also see no use for 214a and 214b whatsoever. Both are extremely minus on block, can't be used in (practical) combos and although 214b charged is overhead, it's super slow and if it's blocked, it's even more minus.
You could close in some distance with 214A or rather j.214A for a better recovery but 214A works too sometimes. You could block after if its blocked so they are relatively safe except maybe 214B. 214[ B ] is one of those overheads you throw out once in 50 matches anyways since its so slow.
Wasn't the best damage output for H Nanaya's shield was to 214[A] after it or something?
It's shield into 214[ B ] and thats corner specific since it wallslams.
You could go for 214A combos since they do the most damage but its not by a large margin that you would want to go for it off every hitconfirm. 2C 236A combos are more notable since they are actually a lot easier and if you used most of your attacks in the string then a 2C 236A launch would do more than just 5A 6A. I also think you get more meter off the 236A variant but I actually haven't tested all his variants to be sure.
For his 5A 6AA, I think midscreen if would crossup if you had 2 or less hits before his 5A 6AA will cause him to crossup and if you had 3 hits (excluding jump in attacks) before 5A 6AA then he would stay on the same side. Of course this would only apply if it was on hit. Though in the corner he would stay on one side consistently.