The only direct route from Faro to Salamanca by public transport is the service operated by alsa.es.
Dept Faro: 01:45
Arr: Salamanca: 16:30
Bus Change at ALBERGARIA (Same Company)
There is an also the option of train:
Dept: Faro 09:05
Arr: Lisbon Gare Oriente 13:06
Dept: Lisbon Gare Oriente 16:06
Arr: Salamanca 00:05
There is no direct train between Seville and Salamanca.
You would need to route via Madrid.
Note: Faro - Salamanca by Car is about 7 hours with stops.
Hope this helps.