See this page:
http://www.metrolisboa.pt/Default.aspx?tabid=533
First trains depart respective terminals at 06.30
Last trains depart respective terminals at 01:00
Weekend trains times depend on which line/lines you are using. They vary between 08:00 minutes and 11:00 minutes between trains, according to the site .
Early morning taxi from Hotel to Airport - Get the Hotel to get one for you and confirm the price, and write it down. There may be surcharges for bags and night surcharge. If any problem at the airport, call a policeman...there are usually a lot on duty outside arrivals and they have been cracking down on taxis recently.