Oct. 1: We're starting the last leg of our trip. Good thing! We're on our last legs! We sailed between Corsica and Sardinia to this Mediterranean port in the second-largest country in Western Europe. We're about 75 miles south of the French border,but we're not in France!

(Barcelona, Spain?)

Oct. 3: Spending our last day in the western-most country of continental Europe. We fly home from its capital tonight. See you soon!
(?)I have no idea about the last one. Portugal?

Oct. 1 -- correct

Oct. 3 -- Yes, Portugal is the westernmost country of continental Europe. What is its capital? (Hint: Google capital Portugal.

Based on the given information, the answer to the first question is Barcelona, Spain. To arrive at this answer, we need to identify the Mediterranean port located between Corsica and Sardinia that is not in France but is about 75 miles south of the French border. Barcelona fits these criteria as it is a Mediterranean port in Spain that is situated approximately 75 miles south of the French border.

For the second question, the answer is Portugal. The clue provided states that the location is the western-most country of continental Europe, and the capital city is where they will be flying back home from. Portugal is known to be the western-most country of mainland Europe, and its capital city is Lisbon.