Are you asking as a tenant or as an owner?
If asking as a tenant as long as the fees are detailed in the lease and it is mutually agreed upon it is not illegal. There could be a grey area if the admin fee wasn't listed in the ad and then added to the lease upon signing.
If asking as an owner there should be a Management Agreement between the two parties. If the admin fee is not disclosed to the owner I don't know if this is illegal but I would definitely look for a new company. Increasing the rent for the tenant by adding the admin fee is not in the best interest of an owner (obviously a lower monthly rent will rent faster and more often) and the management company is not looking out for the owner.
In the situation above is the Administrative Fee the same as the Pet Damage Guarantee, it seems like the wording favors the PM company. Most of the time when you hire a PM company you are using their vendors and contractors.
There are lots of regulations between tenants and landlords but there are not as many for Owners and PM Companies. You don't need a license, continuing education or even a degree to be a PM company.