1. Probably.
2. Cellular voice uses low bit rate audio codecs around 10kbit/s.Clearly you can't get a 14.4 kbit/s or higher fax machine to work over that. Most SIP providers use 64 kbit/s PCM, the same as POTS inter-office circuits. ("office" in the US telco sense.) I don't often need to send faxes but on the few occasions I have, there has been no problem with my Brother 4510, OBi110, Asterisk, VDSL (45 Mbit/s down, 9 Mbit/s up), Localphone UK route to a fax machine on a POTS line in rural Japan.
3. No.