Not 100% sure about this and it probably depends on your hardware or software but I think if you leave 'Display name' in SIP settings blank no ID will be sent. It's probably worth trying to make sure. If you don't have a SIP account yet let me know and I'll see if I can check this for you.
Depends on the provider, In asterisk selecting anonymous will hide it, I have had challenges doing it on IP phones in the past but a simple call to the VOIP provider will normally resolve that as they can often force it from there side!