Portugal then Malagua-need advice

You don't need or want a car in either Porto or Lisbon. The train is easy between the two cities and both have good public transport and inexpensive taxis. If you must see Porto and haven't booked your flights, you might want to fly into Porto as it will save a lot of time.

Also, taking the train from Lisbon to the Algarve is easy and inexpensive. And, renting a car once in the Algarve will save you money and stress of driving out of Lisbon.

I'm assuming you are talking about Malaga, Spain.... Renting a car in Portugal and dropping off in Spain is very expensive. The best way to get from the Algarve to Malaga is likely the bus or flying. Faro has a good size airport but I don't know how quick and easy the flights would be. A bus is cheap but likely a pretty long ride. If you use Rome2rio, it will give you options and costs for each different mode of transportation.

Auto Europe is a great company for car rental. I've used them in many countries for many years and have always been pleased with their service.

Lastly, trying to do Porto, Lisbon and the Algarve in nine days will entail spending a lot of time traveling and not much time enjoying your destinations. You might want to consider saving Porto for another trip.

Porto - Lisbon - Algarve in 9 days isn't very feasible unless you want to spend more time in transit than actually sightseeing.

Kathryn's post above is very sensible.

Travel between Spain and Portugal isn't easy unless you drive. There are no direct flights from Faro (Algarve) to Malaga, only from Lisbon. No trains either.

If you cut the Algarve and stayed in Lisbon and Porto, this would be easier for your onward flight to Malaga. Plenty of beaches and golf around Lisbon instead.

One way car hire will cost hundreds of euros from Portugal to Spain.