When I connect my headset to the phone all of the ring, notification and alarm signals go through the headset speaker. This makes it quite hard to hear the phone ringing when I take of the headset while it's still connected to the phone. Is it possible to choose that all ring, notification and alarm signals always should go through the phone speaker even when a headset is connected?
No. Once a bluetooth device has successfully connected to the phone, it determines that you want to have the ringer pumped through the connection.
The only other distinction the phone makes while connected to a bluetooth device is whether or not it is A2DP enabled. If it is not A2DP enabled, music will play through the phone's speaker while the ringer will still go to the bluetooth device.
Depending on how long you plan on taking off the headset, you could turn off bluetooth for the duration. This can be done very quickly using an app that pins the Bluetooth settings page to your start screen. I personally use Network Dashboard (link below) and it allows me to toggle bluetooth on and off pretty quickly.
Marketplace: Network Dashboard http://www.windowsphone.com/en-US/apps/96e6649a-5582-45a3-9c5b-a71881e18334
No, this is currently not possible. Also, in the Windows Phone 7.1 SDK there is no way to determine where sound is played: if a headset (cable or bluetooth) is connected, sound will be there, else the on board speaker is used. Hope this changes, because I have a software need for being able to make sounds on one, the other or both.