Почему They told me: „We were really happy“ меняем на They told me that they had been really happy? Какие это времена?

В косвенной речи: после глаголов asked, said, told и тд в прошедшем времени!!! мы применяем правило согласования времен, когда глаголы становятся "старше": Cook - > cooked, is busy - > was busy, will take - > would take, has done - > had done.

В данном случае Past Simple меняем на past perfect: were - > had been