Is this expected to happen while asleep? I always knew that, while asleep, stuff like processing words and/or reading texts could not be done by the brain. I'm not even a student in the area, so by knew you could understand as vulgar knowledge.

What I noticed many times is that in my dreams I read and pay attention to words, and the most recent case was right today, when I composed a verse making fun of an existent melody (to put in context, is when you want to mock a song in some way). While the context of the verse and dream was given to my subconscious by my recent obsession about missing playing poker with my friends, what seemed unusual to me is that I did that in a vivid way to the point I remember it letter by letter (and laugh about).

The reason I ask about this is: Is this an expected thing that happens while asleep or could be a sign of a health problem? (don't know: stress, insomnia, or even something I should worry about)

An appropriate answer should be backed by a meaningful and reputed research result.
The appropriate answer is that dreams are generally not in any way diagnostic of a health issue. Being able to read while dreaming is absolutely not diagnostic. I can't imagine that any reputable research has been done on this topic.