Yes you can use fax with elastix server. if you going to use it like a normal fax machine you will need a pstn lines (analog) to send and recived faxes, if you want to use it with VoIP server provider you need to be sure firts that your provider support T38 (fax suppport), because if he dosent support it you wont be able to recived and send any faxes over voip.
Wrong, fax over ip works, but it's not too reliable. I'd say 80% work, but you must use a low compression codec, as g711 or slin.
Anyway, Elastix doesn't support T38 termination, as it's based in Asterisk 1.4. It supports T38 passthrough, so you can connect a T38 capable gateway to terminate T38 faxes.
If you really need your PBX to terminate T38 faxes, you'll need to try Asterisk 1.6, Callweaver or Switchbox.