How does monitor resolution affect how your computer performance

All of those situations is mainly going to be your cpu provided you have at least a baseline gpu solution like an Intel HD graphics. Gaming will require more gpu power of course and the resoltion will affect performance greatly on the gpu, on the cpu however resolution switch will not be as significant in affecting performance.

Java has very limmited gpu support but is starting to have dx support which will allow the gpu to do more but is still limited. Resolution will not really affect cpu or gpu performance unless its in a graphic heavy environment which still wouldn't be much.

Movies performance comes from the gpu and support of higher resolution movies will require better gpus but generally the baseline gpu that comes with a computer should be able to do 1080p decently well.

Overall performance is going to be mainly limited by your cpu but also your ram and hard drive performance. Getting enough ram and an ssd is a lot more important then a top of the line cpu in the point.

The APU's from AMD are great for any decent all arround performance, given decent cpu performance and decent gpu performance that makes it very good for general computing and light gaming.