Wow, You want to do a lot!
I would suggest the following:
Day 1 - Faro Airport to Tavira - 1 hour - Motorway all the way.
Day 2 - Tavira to Salema - 1:45 hours - if you take your time. Motorway to Lagos and then EN 125 motoroad. In the evening nip over to Sagres (20 kms) to see the sunset at Cape St. Vincent. - The most south westerly point of Europe.
Day 3 - Salema - Vila de Bispo - Aljezur - Odeceixe - Odemira - Grandola/Alcacer/Evora or Beja/Evora - Good 3 metre roads all the way - Time 4 to 5 hours with stops and dawdling.
Evora to Lisbon via Vasco da Gama bridge will take about 2 - 2,5 hrs. I suggest you try to drop the car off at Gare de Oriente if the agency has an office there as this will avoid having to drive into Lisbon or the Airport. You can then get train via Entrecampos to Sintra or Metro into Lisbon.
Note the main Rossio train station for Sintra is currently closed for tunnel works. Trains leave from Entrecampos.
The rest of the trip sounds fine although you need to check public transport links to Spain from Aveiro. (You may get better connections from Porto.)
