Are tenants legally required to hand over keys to the landlords property management team? Or is that the landlords responsibility?

What are my legal rights as a tenant:

The landlord is claiming that she is out money for not being able to rent out the place I moved out of because I did not provide access.

1. Is it my responsibility (the tenant) to provide a key to the property management company or is it the landlords responsibility to provide a key?
2. How much notice does the property management company have to give me for showings?
3. Can a property management company legally act on behalf of the landlord without a written contract? Like if the landlord just verbally asked if the property management can take over the property, without confirming they were hiring them. (The reason for this question is because, I believe the landlord only inquired with the property management company and never actually confirmed contracting their services). So technically I wouldn’t be responsible to work with the property management company for viewings, etc. Since they were not actually hired while I lived there. So if I was responsible for handing over the key, then I wouldn’t have been required to do so until after the company was actually hired.