Since the latest patch of the game, you are now able to use the Inherit Skill feature, which allows you to make one of your character inherit up to 3 skills from another character, at the cost of losing this unit.
Can a single character inherit as many skills as he wants, or is there a number limit?
1 Answer
There is no limit to the number of skills a character can inherit from other characters, as long your character is compatible with those skills (a mage won't learn a sword skill) and in the limit of three skills per sacrified character. So you can inherit as many skills as you want without fearing that you could have created a better character with other sacrifices.
It is confirmed on the Fire Emblem Heroes' wiki:
1There is no limit to how many skills a Hero can inherit overall. However, each sacrificed Hero can only provide up to 3 inheritable skills.