If I buy a Brother MFC-7300C, would the fax portion of it work in 
Mexico?  (The company didn't know whether the US country code to which
the machine is set is compatible with Mexico's phone system.) If I
wait until I go back to Mexico,is the MFC-7300C available in Ciudad
Victoria, Tamaulipas, and at what peso cost?  Is servicing available
in Cd. Victoria and where?  I must decide very soon.

Yes, the Brother MFC-7300C's fax portion will work in Mexico.  Feel
free to call their toll-free customer service in Mexico
01-800-759-8000.

If you buy the Multi in Laredo, TX, you can have it serviced there. 
However, you must pay import taxes for Mexican Customs when you bring
it.  Depending on how often you go to Laredo, you might consider
buying it in Cd. Victoria.

There are a lot of places that sell Brother equipment in Cd. Victoria:

http://www.seccionamarilla.com.mx/Listados_indirectos.asp?estado=Tamaulipas|TAMS&QueryText=344173%3CIN%3ECategorias%3CAND%3E%28%3CSTEM%3ECOMPUTADORAS%3CIN%3ENombreCategoria%3CAND%3E%28ciudad%3CAND%3Evictoria%29%3CIN%3EPoblacion%29&catname=Computadoras+Mantenimiento+y+Reparaci%F3n+de&EstadoVerity=Tamaulipas|TAMS

Find a "Centro de Servicio Autorizado" (Authorized Service Center),
and ask them about your specific concerns.

InterCuatro in Chihuahua, Mexico, priced me a MFC-7300c at 4025 pesos
(includes %15 tax)  Feel free to contact them in Mexico at
01-614-424-3380 (Spanish only).

I hope this works for you.