Help with itimerary

Can’t help with your itinerary but train tickets can be purchased online directly from the Portuguese rail. www.cp.pt Discounts available up to 5 days advance purchase.

I would suggest you spend a few days in the Algarve with a car, but don’t pick it up until you get there. The train from Lisbon to the Algarve is easy and cheap. Plus, that eliminates having to drive in the Lisbon area. Lagos is my favorite town in the Algarve, and from there, you can visit the western coast. There are some lovely days that time of year, and some not so lovely.

From the Algarve, you could drive to Evora and spend a few nights. Keep the car in Evora so you can drive to some of the wineries, if you wish. Then drop the car there and train back to Lisbon.

In Evora, there is a tour of the megaliths outside of town led by an archeologist. It’s a great afternoon and I highly recommend it.
In Coimbra, GoWalks has a great city tour that includes the university and library for a reasonable fee.

It seems as though you have somewhat rushed through your first two weeks, so might want to slow down a bit in the last week or so. More time in Lisbon, or even a few days in Cascais might be good. Cascais is great that time of year with few tourists. Of course, the entire time you are here, you will (hopefully because of the drought) have to deal with rainy days. But, there are also glorious warm days with brilliant sunshine when you can eat on the beach or outside on a miradouro with great views.