Is the violin hard to learn? Can the violin be self-taught?

You can learn ANYTHING without a teacher. Teachers do not posses secret knowledge, or magical powers to grant special abilities.

All we do is help you learn the most effective things in the proper order, as quickly as possible.

...however....

There are some things which simply take a long time to do or learn.

You could learn about physics without ever cracking a textbook or asking anyone else, but you would have to replicate Newton's discoveries from first principles and go from there. It would take you a lot of time and trouble. You might not have enough lifetime left to do it all by yourself.

You could learn how to mine and smelt metals, but without the benefit of centuries of human development, it would be tough to do it from scratch.

You could build your own car, or airplane, or boat. Those craft vehicles are unbelievably time consuming and expensive and require a lot of existing parts. Imagine trying to build a car right from the base metals.

All of these activities are things you can attempt by reading, checking out Youtube videos, experimenting with, and generally failing at multiple times before succeeding. All are possible, for you or anyone else. Many self help resources make these tasks much faster and more practical.

They still will take you a long time.

So will learning to play the violin.

No level of difficulty in learning a new instrument or pursuing a passion or hobby is worth more than being finally able to have done it. And the Violin is the most rarest and most beautiful instrument one can ever possess . It's melodious and soothing. And to your second question I would say yes you can teach yourself but when it comes to professional playing (playing the right way - the position. The spot where you place your fingers and your posture and reading your notes well cannot be mastered by yourself with yourself. You will need proper guidance at least till the basics are clear). Once you know how to read until a certain level you can take a call on whether you want to carry on by ear and play by yourself or be so confident that you'll be able to learn the technical part too on your own and your good to go.