No you don't get to speak to the client or get his number as this would defeat the purpose of the agency.If you were vetting the client yourself why would you need the agency?Also the client expects to deal with the agency not the lady nor would he want various ladies on agency sites to have his number or he would book an indy.The agency is the middle man between you and the client any queries and you ask the agency who then queries it with the client.If you are using your own place for incalls then yes they give the client your address.However some agencies have their own incall places or only offer outcall.
The agency agrees a rota with you and expect you to be free when you are on rota unless you tell them otherwise but if you kept not being free when you have agreed you are on their books between say 10am and 10pm then they are going to think you unreliable.Unless you are also working as an indy and they are ok with this in which case you would text and say 'busy between 1pm and 2pm' so they know not to send you a job at this time.
How do you give the agency their share?Usually you put it in their bank account.Although some may have other arrangments.

Why would you want to? I really struggle to see any benefits from doing so.

The benefit I can see is the access to an incall place, but for me the downsides outweigh that (for now).

No you don't get to speak to the client or get his number as this would defeat the purpose of the agency.If you were vetting the client yourself why would you need the agency?Also the client expects to deal with the agency not the lady nor would he want various ladies on agency sites to have his number or he would book an indy.The agency is the middle man between you and the client any queries and you ask the agency who then queries it with the client.If you are using your own place for incalls then yes they give the client your address.However some agencies have their own incall places or only offer outcall.
The agency agrees a rota with you and expect you to be free when you are on rota unless you tell them otherwise but if you kept not being free when you have agreed you are on their books between say 10am and 10pm then they are going to think you unreliable.Unless you are also working as an indy and they are ok with this in which case you would text and say 'busy between 1pm and 2pm' so they know not to send you a job at this time.
How do you give the agency their share?Usually you put it in their bank account.Although some may have other arrangments.

Thank you bibio