From my personal experience, I have to say the second one. In less than a year I acquired a level of fluency in French that I had never had in my many years studying English. However, it is not always that easy to spend a year abroad, especially when you get older and have a family. But can you improve or master a foreign language just studying it from at home in your own country? Sure you can! Especially nowadays, with all of the excellent resources that we have available. It may take longer, or require a greater effort to do so, but it can be done, as I hope to demonstrate in the coming months as I continue to improve my English.
Finally, the “half language” I can speak is Italian. I say “half” because I studied Italian in a language school here in Barcelona many years ago, but just for one year. Anyway, Italian has a lot in common with Spanish and Catalan (and even with French), so it is an “easy language” for me to learn. Of course, there are no truly “easy” languages, but I could say that it is far easier for me than, for example, German.
I can understand Italian more or less if the speaker does not speak really fast or use a lot of slang, and I can say some basic things in Italian.
Another similar example would be Portuguese, which I have never studied and I don’t speak, but because of the similarities with my languages, I can more or less understand a conversation. For example, I remember when I went to Lisbon for a week of vacation some years ago—I could made myself understood and I could ask some basic things, having just learnt some very basic vocabulary (like hello, goodbye, excuse me, thank you, coffee, milk, etc.) Of course, I do not consider Portuguese as one of my foreign languages. Or at least, not yet.
However, maybe after dealing with German and improving my Italian... who knows?