I have a requirement to answer an incoming call through the SDK, and for the call to be established on the handset, with the user using a headset connected to the handset. We want this to happen without further user interaction (only a button click on the application). Is this possible?

We are also wanting to Place a call, and have this automatically transfer as well (again without any further steps for the user).

Answering a call:
I can answer a call via the SDK (IncomingCall.Accept()), but this receives the call on the application, not the handset. If the user wants to connect via the headset, they must currently:
- press the button on the headset
- select the incoming line that has been established

Placing a call:
Similar to above. I can place a call, but currently the user must make the same two steps in order to transfer to the headset.

Is it possible to place or answer a call via the SDK and have it automatically transferred to the headset?
Thanks.

Could you please provide more info about your environment? Do you use Headset API for interaction with handset or it is different device (Avaya phone) that has been registered om the same extension as Client SDK application (MDA) or you have registered Client SDK in shared control mode to control your device?

If you want to control a desk phone to accept the call remotely, then you need to connect Client SDK in shared control mode:
https://www.devconnectprogram.com/site/global/products_resources/avaya_client_sdk/programming_docs/current/windows/communication/api_refs/html/T_Avaya_ClientServices_SharedControlService.htm
If you place the call from Client SDK then it will be placed on controllable device. If you end the call on Client SDK, then it will be ended on the controllable device also.