A Specific Cursed Item generally costs a fraction of the real item to craft, often around 10% (Incense of Meditation 4,900 gp, Incense of Obsession 500 gp) or 20% (+2 Sword 8,315 gp, Cursed -2 Sword 1,500 gp). An exception is if the item is especially useful, such as the Scarab of Death (80,000 gp) which could be given to an enemy to kill him in one round.
A normally functioning item with a drawback or dependent curse condition (e.g. only works in the hands of a creature with a particular alignment) should reduce the cost by around 10% to 30%, or more depending on severity. The crafting guidelines state that an item reduces in price by 10% if they require the wielder to have a certain skill, and 30% to have a certain class or alignment. You shouldn't let players pick this as a drawback while crafting, since a wizard can just create himself a staff only usable by wizards for a big discount at no penalty.
The spells remove curse and break enchantment only free a person from a cursed item, but do not turn the item into an uncursed version of itself. Since the price difference between a cursed item and its uncursed version is significant, a single spell shouldn't be enough to repair it permanently, although wish can repair items at an XP cost. A wizard with the correct item crafting feat could probably repair a cursed item by paying the difference.
Note that while remove curse does remove a curse from any item except a weapon, shield or armour, it doesn't necessarily turn the item into a properly working version. The item may have been created cursed by accident, or have broken somehow and lost its original power.
An alternative way of creating a cursed item appears in Dragon Magazine #348, October 2006, in the article "Bestowed Curses". The spell bestow curse can turn a weapon into a cursed item of its kind, so a +4 sword becomes a -4 sword. Since bestow curse is a Permanent duration spell, rather than Instantaneous, an item temporarily cursed in this manner returns to its original form when the curse is broken.
Since all of the Detect spells have a duration of Concentration, it seems to me like you have to concentrate to gain a benefit from them. If the Night Hag concentrates for 1 round, she can use any of her detect spells without having to cast it, but she doesn't get any information without concentrating. The difference here between continuous and at will is that the continuous version doesn't provoke an attack of opportunity. I don't think there's a solid rule on this, but I feel like this solution fits the normal behavior of the spells best.
Best Answer
Make it so that the curse is still tempting. He'll discover the curse, but make the item useful enough that the party will keep it around just in case the curse is worth it.
Requirements or Drawbacks are good ways of doing this. A Sun Blade that causes a constant solar eclipse in a mile radius, a healing wand that moans in pain and requires you wound yourself for 5HP each time you use it, or a staff with a statuette on top that weeps blood and must be washed in holy water to make it work.
You'll want to balance the item's utility and curse so that even knowing the curse the person is tempted to use it, but not make the item so useful that it's automatically worth dealing with the curse. I find that this temptation is stronger if you give your players exact numbers: "Each time you use it roll a d20 and the curse triggers on a 1" is far more tempting than "there's some mysterious chance that the curse triggers whenever you use it."
Items like this will be far more effective if you make it clear that there's no curse compelling them to keep using the item. Something is much more tempting if you can quit at any time. If they need to use remove curse to get rid of the item, most players will immediately reject it.