For the first thing - you can check it with a simply SIP softphone.
For the second - yes, for sure. Cisco IP phones (loaded with a SIP image) work with any kind of SIP proxy - MIND CTI (B2BUA), NexTone, SER, Asterisk and etc.
Do you have good URL on how to load SIP image on 7960 without using Cisco callmanager.
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