2)Info: A part of your problem may be caused by thinking of "greedy problems". There are greedy algorithms and problems where there is a greedy algorithm, that leads to an optimal solution. There are other hard problems that can also be solved by greedy algorithms but the result will not necessarily be optimal.
1)Info: "A term used to describe a family of algorithms. Most algorithms try to reach some "good" configuration from some initial configuration, making only legal moves. There is often some measure of "goodness" of the solution (assuming one is found). The greedy algorithm always tries to perform the best legal move it can. Note that this criterion is local: the greedy algorithm doesn't "think ahead", agreeing to perform some mediocre-looking move now, which will allow better moves later.