1. “学会了” is a fixed phrase to express "sb has got to learn sth". "会了" means you not only tried to learn it and really gained the knowledge or skilled taught. For example, "我学会了这些词" means I learned these words and now I can remember them, understand them and use them properly.
You can also say “看会了” or "听会了", if you want to emphasize the way you learned it is observing or listening only. For example, 我没看乐谱就听会了这首歌.
2. "v+完了" means finished/completed. For example, “我学完了这些词” means I've finished studying all these words. "我看完了一本书" means I've finished reading a whole book.
3. "了" itself is a quite flexible and subtle auxiliary word, it is usually used after the verb to indicate that the action has already happened. “学了” doesn't have to mean "学会了", otherwise all students will get full mark on what they learned.