Does our neighbor have the right to demand a sum of money in exchange for cleaning the building's staircase for past years, especially since she did not inform us of that beforehand and the requested amount is exaggerated?

You are not obliged to pay for the cleaning of the building's staircase, especially since you were traveling, and a traveler does not use the staircase. What must be paid on your behalf without your permission is that which was obligatory for you and was paid with the intention of being reimbursed by you. As for what is not obligatory, or what the payer did not intend to be reimbursed by its owner, it is not to be paid. So, whoever fulfills an obligation on behalf of another with the intention of reimbursement, shall be reimbursed, otherwise not.