The current answering mode is set on the phone, rather than within CAD.
If you touch the Headset button on the phone and get dialtone, and then touch End Call, you'll notice the phone hangs up and returns to idle, but the Headset light stays on. That leaves you in headset mode. Now if a call comes in and you touch the Answer softkey on the phone, it will answer to headset rather than the default mode of speaker. And likewise, CAD CTI commanded answer will answer to the headset.
I don't think so. From CCMAdmin you can knock out the speakerphone entirely, but from memory I don't think that's going to force headset mode. You can set a line to auto-answer to headset (or to speaker) explicitly, but auto-answer is only appropriate in very specific environments. This is typically handled with just a few minutes of user training.
(adding) To be clear, headset mode will stay on until the user chooses to turn it off. You don't have to do it for every call.