The balcony in front of the building is cracked and the windows are breathable. Is it illegal for a property not to pay property fees? Does the property have the right to sue?

The law does not stipulate that not paying property fees is illegal, and at most it is a breach of contract. The property may sue the court to ask you to pay the property fee according to the contract, but you can get the contract. Since there is a charge, there must be a contract. If the situation you mentioned belongs to the scope of property responsibility, you can also refuse to perform the contract, refuse to pay the fee and collect the evidence on the grounds that the property service is not up to standard.