1). the difference between finding the limit of x=c and actually plugging in the number x=c has to do with what you're trying to figure out. when you're finding the limit you are actually looking for numbers as you get closer to x=c.in other words your trying to get somewhat of a picture of how the function is going to look like. when you're plugging in x=c you are finding actual points and therefore you will be able to graph the function. this will be the actual way the function looks like.
also the two are the same when the limit of f(x) as x->c- and f(x)
as x->c+ are equal to f(x) as x->c.
2).the major similarity between finding the derivitive and the slope of a line is that you're finding the slpoe of a line. the difference is that for the derivative you're trying to find the slope of a specific line, a tangent line.