1) How would I pronounce "huius"? I'm thinking "hwee-oos"?
The hui diphthong does not have a comparable sound in English, pronounced sort of like hoof, but change the F to a Y. Add to this hui a yus sound and you have it.
Making sentences here, how did I do:
2) Nōmen huius mōris perfidia est. = The name of this custom is treachery.
This sounds quite odd to me... treachery is hardly a custom, no matter who you are. A better word might be "behavior".
3) Virtūtēs hominum mōrēs fēminārum sunt. = The virtues of men are the habits of women.
The translation doesn't really make sense, but it's hard to know what it means without context in this case. Perhaps it is something like "Mankind's virtue is the character of women"
4) Nūllae hae uxōrēs tempus habent. = None of these wives have time.
5) Ea nōmīnis egēbat. = She was in need of a name.
6) Rōmānī castitātem virginum cōgitāvērunt. = Romans thought of the chastity of the virgin.
Normally cogito without a preposition means "ponder, reflect upon, consider, plan" or something like that. Commonly found with de, then it would certainly mean to think of.
MVLTAS GRATIAS VALETEQVE BENE!
You're getting them all right. You should probably work on kneading out some of the awkwardness. I used to translate more strictly than you do and it just looks much better if you go over and then make some adjustments, keeping it true to the Latin as possible but also making sure it isn't nonsense.
flebile nescio quid queritur lyra, flebile lingua murmurat exanimis, respondent flebile ripae