Is it permissible to kill desert reptiles and birds by injection while they are alive for the purpose of taxidermy, whether for teaching or laboratory decoration, even if the Basmalah and Takbir are recited during the taxidermy process?

What you are doing is not a proper slaughter (tadhkiyah) of animals, even if you pronounce God's name over them. The ritual slaughter of an animal that can be controlled is only valid if performed at the throat and the upper chest (labba). As for killing animals in the manner mentioned for the purpose of scientific experiments, it is permissible because it serves a legitimate and beneficial purpose. If it were possible to conduct experiments on animals that have been ritually slaughtered, that would be preferable to avoid the disagreement regarding the utilization of a carcass (maytah). However, killing them merely to decorate the laboratory is not permissible.