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Kamailio is a SIP server, implementing the specifications from RFC3261. Its root functionality is routing any kind of SIP packets. On top of that, many conceptual features are implemented, see more at:
No, however Kamailio can be configured to proxy media if needed.
Kamailio supports all codecs (even codecs that haven't been created yet).
Since Kamailio is a SIP proxy, it does not handle the media streams. Codecs are negotiated between the two endpoints.
Yes, Kamailio can be used for video calls. The two SIP phones must support video codecs/calling.