if you want to find correct memmory module, the best place to try is crucial click here
as for warrenty, noone know for sure because it is different from different PC maker.
Generally for most PC makers, no problem, but some PC makers put a stick on the case, the opening of case will invalid the warrenty
you need to read warrenty document or contact HP, are you sure it is still under warrenty? It seems this model is rather old.