For the "rules", try <a href="http://www.faa.gov" target="_blank">www.faa.gov</a> and follow "Advisory Circulars". Find AC 25-13, you will find your answers. Although not really a "rule", it offers an acceptable means of compliance to allow flex and derated operations, and is widely followed in industry. This is for the US, but there is a similar European equivalent.
As for uptrim, this relates to an APR, ARP or ATTCS system (depending who certified your airplane), where the normal takeoff setting is actually a derate from the FAR 33 certified maximum takeoff power. This automatic function will "uptrim" the good engine on takeoff when the other one falls over, thus giving additional thrust. This uptrim is conventionally allowed to be up to 10% of takeoff thrust, but is not in excess of the max takeoff thrust certified for the engine. Normally only found on twins, I think that Boeing started it. Try FAR 25 Appendix I for this rule (this one IS a rule!).