The books sais that,if you fail the test, you get another chance on the next levels with a +1 difficulty. But the spanish book doesn't leave clear if you have to pay to have that new chance once again, or you can check on the next initiation for free. What's the solution?

You shouldn't have to pay for the chance at the next initiation.

Also, when fail to learn a metamagic, you can basically try to learn that same one again 'for free' at your next initiation.

Have you tried mailing the FAQ?

Nope. Should have, but I'm lazy this days due to exams, and I was reading around here when I remembered, so...