Is it true that humans largely have the same psychological reactions when put in the same situations? Do reactions differ in relation to genetic differences, and if so how much? What sort of research has been done on these topics?
No. Two examples:
Some people are comfortable with noises that others cannot tolerate, and genetics plays a part in this.
Genetic Component of Noise Sensitivity, Marja Heinonen-Guzejev, Heikki S. Vuorinen, Helena Mussalo-Rauhamaa, Kauko Heikkilä, https://doi.org/10.1375/twin.8.3.245
Some people are terrified of things that others are not afraid of, and again phobias are partly due to genetics.
Kendler KS, Neale MC, Kessler RC, Heath AC, Eaves LJ. The Genetic Epidemiology of Phobias in Women: The Interrelationship of Agoraphobia, Social Phobia, Situational Phobia, and Simple Phobia. Arch Gen Psychiatry. 1992;49(4):273–281. doi:10.1001/archpsyc.1992.01820040025003