The weather can be quite wet and windy at that time of year. The Algarve is all about the beaches and golf and it isn’t the right time of year for either.
Albufeira is my least favourite place on the Algarve - popular with stag and hen parties out of season because it’s cheap (and characterless). Tavira and Lagos have more character.
Lisbon is great for 5 days at least plus day trips to Sintra and Cascais. Evora is worth an overnight stay.
If you take a hire car into Spain, you will pay a hefty one way drop fee. You may want to fly to Spain or have a car in Portugal and take a bus to Seville then hire another car once you want to move on.