The application needs .NET Framework 4.0 installed. If you don't have it installed, you should download and install it from the Microsoft website.
Problems with drawing appear when the function has many vertical asymptothes, or the function changes values too often, and is described here. Try increasing the graph precision from preferences.
This is a known issue, and has to do with the way the functions are drawn. The slowdown appears when resizing the window, or navigating through the graph. We are working on this issue. What you can try is to decrease the graph precision from the preferences.
You need to verify you haven't accidentally typed a letter where it shouldn't be. You should also check the language article, to learn about the syntax rules of expressions.
You have a syntax error, you need to check the language article, to learn the correct syntax of expressions.
This error usually appears when you didn't give the correct number of parameters to a function. Check this article to verify the parameters.
You should contact the developer using the contact form. Please, include a useful description of what you were doing when the problem has occured, and eventually a link to a screenshot. The log file which should be located in the directory logs, where the application executable is, would also be very useful.