When traveling by train from Tangier to Fez, is it necessary to change trains anywhere? And what is the cost?

Looks like you have to change at Sidi Kacem.

Go here for details and to find the fares which vary according to class of service you choose. This website is in French, but it's pretty obvious what you have to do to get the information:

http://goafrica.about.com/gi/dynamic/offsite.htm?zi=1/XJ&sdn=goafrica&cdn=travel&tm=28&f=10&su=p531.25.1 52.ip_p532.6.150.ip_p284.7.420.ip_p284.5.420.ip_p5 31.23.420.ip_&tt=2&bt=0&bts=0&zu=http%3A//www.oncf.ma/scripts/horaires1.asp

ONCF (Morrocan Railways) official website is
http://www.oncf.org.ma

You can probably also find links at the Moroccan Tourism site:
http://www.tourism-in-morocco.com/
Information is available in English, French or German.