1) Frao Airport is about 8km from Faro Station. You will either need to get a bus (infrequent) or a cab to Faro Station.
2) The easiest route from Lagos to Almeira would be as follows:
a) DAMAS/EVA bus from Lagos to Seville
http://thomasallen.home.sapo.pt/travel/001.htm
b) Seville to Almeira - I have uploaded the alsa.es timetable here:
http://www.scribd.com/share/upload/10765936/eicrue3bioiiujw30o1
Some buses route via Malaga so you might want to lay over.
