Hello:
I've been on an internship in the city hall of my city for 4 months as part of a web development course I joined. The internship is unluckily not very related to web development, so my classmates and me are assigned various tasks depending on our knowledge.

I've been assigned tasks related to my previous studies at vocational school. Contrary to the ones my classmates are assigned, my tasks are usually more complex to do and require to know about the subject. We used to be in a separate room before, but I'm currently not working with my classmates. I'm sitting where the rest of the city hall's employees work.

I feel extremely integrated when I'm there. I've never felt like this before and I'm glad I decided to join. It has also helped me to develop my social skills, especially after so many months not going out.

My mentor is a nice person. He's kind and supportive. He has helped a lot of students with their problems. And I don't mean problems related to the course, but personal ones. He has given me a lot of advice when I needed it as well. He's not the one who assigns me the tasks, but a man who is sitting next to him. And that man happens to have studied the very same things I have, and shares some interests with me. Interests I've never found people to have. He gives me advice sometimes, too. But his advice is focused on my career and how to make progress. He's also full of jokes and doesn't seem to care about my age when he jokes.

Yesterday while we were waiting for a server to reboot, we talked about things like where he is from, what he studied... and I told him that I'm good at what we were doing because rather than going out I like staying at home and research on the Internet and read books about it. He told me I do well by doing so. Then, I told him about my uncommon interests like reading the things I mentioned I like researching and he told me he has uncommon interests as well. For example, he's currently doing stone-looking panels with cement and a silicone mold to put them on a wall.

Would it be awkward if I tried to befriend them? I'm not saying I want us to meet them outside work or something similar. But for example, I would like to know how this man is doing with his stone-looking panels and see how it looks like.

To be honest, apart from looking awkward or desperate what makes me doubt about it is the fact that one of them is our mentor. What if he or my classmates believe I'm trying to brown-nose him? And they're older than me, of course. My mentor is 30 years older. I'm not sure about the other man, but he must be 25-30 years older as well.

What should I do?