If a hero gets a cursed item, like the Backbiter, can the hero use a doll to remove the curse token and keep the item equipped? If so would the hero again get the curse token if the item was unequipped and then re-equipped again?

Yes he can remove it. And yes if he dies he is either forced to immediately re equip the time (hence receive the curse again) or to discard it. In my game if we are going to give someone a cursed weapon it will probably be the tank that is VERY unlikely to die and if he ever ends up with 2 curse tokens then you can use the cursed doll as you remove 2 effect tokens it's better used when for some reason you have 2 on you. (I remember tahlia with unmovable and a skull shield with the cursed sword spraying death in her path and with no curse token on her).

Sidenote if you are playing RTL which i don't know if you are it is not money efficient to be using 200 for a doll each time to use a cursed item.

It's important to realize that you gain curse tokens from the act of equipping a cursed item, not as a result of having it currently equipped.

If you equip a cursed item, you gain a curse token. If you unequip that item, you still have a curse token. If you equip the same item again, you now have 2 curse tokens.

When you die, you lose all your curse tokens (after losing extra conquest for each one), but any cursed items that were equipped must either be re-equipped (causing you to gain new curse tokens) or discarded (and lost forever).

A curse doll removes tokens from you instantly. It dosn't stop you from gaining tokens at any future time.