we want to break our lease. If we get a "3 days to vacate" notice and vacate in that time frame, are we still liable for the remainder of the lease?
Yes, you remain liable for your contract obligations. If they release the property then you would get a credit for that.
Depends on why they request you vacate.
I guess I would have to argue that in court. If they give you a 3 day notice to pay or leave - then in essence they have broken the lease. However, what does your lease state. This may be covered in the lease and you may have to pay until the unit is re rented or the balance of the lease.