While looking for audio in Russian to record and listen to while doing other things, I stumbled upon this website called MasterRussian.com. It offers some free podcasts about the Russian language and one was put together on Boys and men. I thought it was delivered in a fun and interesting way, and perhaps you will, too. It discusses мужик among other terms for boys and men.
it's quite hard to describe what мужик is translated as, it's kind of both negative and positive depending on the context, who you are and the person you're talking to; though it's not that informal, you're probably best off if you don't use it till you have quite a grasp of the language. Both peasant and tough man are good, though missing some shades of the word, for my taste
When asked to translate я мужчина to english it is, I am a man, but when asked to translate I am a man to Russian the answer required is Я являюсь мужчина. This needs to be corrected. I'll reiterate. "Являюсь" has never been introduced to the lessons in any capacity. Either teach it to us, or remove it from that answer.