I used Google Translate to translate your question as some of your translations are a bit unclear:
What difference do you see between learning and training?
Learn = Pay X trophies, put the skill face up in your area, and you can now use that skill.
Train = Draw X Skill Cards, discard cards down to your hand size.
Is there limit of skills learned by character? Or is it possible to overcome 3 by acquiring objects or skills?
Characters can learn a number of skills of each type (Red, Blue, Yellow) equal to their level in the corresponding attribute.
For example, Lord Hawthorne has 3 Body, 1 Mind and 1 Spirit. So he can learn 3 Red (Body) skills, 1 Yellow (Mind) skill, and 1 Blue (Spirit) skill.
It is possible for Lord Hawthorne to increase these numbers by learning skills or getting assets which have bonuses. For example, Well of Power in this image:
Hawthorne can learn Well of Power. It gives him +1 to Spirit (Blue) so he now has 2 Spirit and can learn 2 Spirit skills (including Well of Power, so he can learn 1 more).
Is it possible that learning does not cost trophies?
Yes - if you reduce a skill to cost 0 trophies, then you can learn it for free. For example by learning the skill called something like "Fast Learner" which reduces the cost of skills by 1. With that skill, skills normally costing 1 trophy will become free to learn.