Also, after I completed some tasks, he started asking me questions
like "Are these tasks challenging or should I give more?".
This sounds like a personal insecurity to me. Often, when I was first teaching, I asked students whether or not they thought I was moving too fast or slow, because I had no idea what pacing would be beneficial. I kept this practice every year, and it seemed to help me and the students to get the most out of class. I could change pace based on the majority of responses and adjust for slower/faster students individually.
I tried asking him why he asked such questions privately and he
remained silent about it, not replying to my messages.
These sorts of questions should be asked face-to-face, especially if he is your mentor. Don't go into it looking for conflict, either. "I wonder if you have any suggestions about my performance and what I should or shouldn't be doing? Do you find my studying to be a problem, or my completion of tasks adequate?" If you approach it as questions that will help you, you're likely to get a much more positive and useful response. If, after you approach this with him, you still feel he's not providing guidance, you can speak to whomever is your intern sponsor and let them know that you're concerned with his silence on subjects which could help you fit in better or learn your position faster. Don't make it about him, simply say you would like to get the most out of training.
The point of internship is to learn, and you can't learn if you don't ask questions. You can't rely on messages to gauge the response to some of those questions, human inflection, body language and the like are required to make a reasonable decision about what they say. "I think you should be fine" can be said sarcastically or heartfelt, and you can't tell one from the other in a message.
Good luck on the internship, and make sure to take control of the situation and make it a positive experience for yourself.