Sevilla to Lisboa

No, there is not a convenient train connection from Sevilla, nor from Merida which takes 6 hours and 2 connections (once daily). You can take a direct bus Sevilla-Lisbon in 8 hours; see www.alsa.es. If you were going to Faro, I'd also take a direct bus from Sevilla, not from Huelva.

How about driving?
Is it easy to rent a car in Spain and return it in Portugal?

Javier,
Have you considered flying from Sevilla to Lisboa?
Check skyscanner.com for cheap flights on this route.

Returning a rental car in a different country is not recommended as there are usually hefty fees associated with such.

rome2rio.com has 2 buses from Sevilla to Faro - Internorte (3.5 hours) and FlixBus (4 hours).

When Priscilla says "hefty" fees, it can be several hundred euros.

Alas, this issue comes up on this board about once a week. We in the US think of Spain and Portugal as practically one country, but they have surprisingly skimpy transit links between them. There are a few trains (often at odd hours), there are buses (fewer than you would expect and often needing more changes than you expect), and there are flights (more than you expect, to make up for the lack of other options). You can drive, but as the above posts say, it can cost several hundred euros extra to pick up a car in one country and drop it in another.

Rome2Rio is a great start for these questions. You should never take it as the last word - always check directly with the website of the airline, bus company, etc (you may need Google Translate). Here's Seville to Lisbon - you'll see what we're all talking about: https://www.rome2rio.com/map/Seville/Lisbon

Is it easy to rent a car in Spain and return it in Portugal?

Easy? Sure. Expensive? OMG yes.

Looks like I could take a bus to Faro and then, the train to Lisbon