How can writers avoid exposition with the restrictions of solely words and not visual art?
It's all about timing the information you're giving. You have to give just enough information to keep the story moving forward, without giving away too much. Since the information is relevant right then and there, it's much easier to work it into the story, and imply it through showing. If you're struggling to fit a lot of information in, odds are, it's not all necessary. It's a balance of withholding information until the right point to let it escape.
How can we show our audience with visuals rather than explanation.
I ask the question, "can the camera see it?" It's not a perfect exercise, but it helps a lot. If you want to get across that your main character is this really likable guy, then you have to think about how the camera would pick it up. Take, How to Train Your Dragon, as an example. You could simply say, "Hiccup didn't have the best relationship with his dad as he struggled to find his place in the village", but it wouldn't mean anything. Instead, they show the relationship through arguments, discussions, Hiccup sneaking out of the house despite his dad's orders, and so on and so forth. If you're telling and not sure what to do, ask yourself if the camera could see it. It's all about visual examples.
How can writers include a minority character (to involve a sense of social conciousness) without pointing it out and being offensive?
I think the answer is to not imply anything at all, to any character. Well, gender is an obvious exception, but don't imply a character's race at all. Let the reader decide how they look. A woman approached J.K. Rowling and told her that she could see all of the characters so clearly. When asked how she saw they characters, she described Neville as a black guy with long dreads. If the movie is anything to go by, then that's just about the opposite of what he really looks like, but it didn't matter. You wouldn't describe a person who isn't a minority, so any description claiming that they are isn't really good. Just let the reader decide how they look like.
Of course, if race is a conflict, then it's necessary to bring it in. If it's not essential to the plot, then don't expand upon it.