As to Shiluach HaKan as well as not using an ox and a donkey as a team to plow – some believe that these mitzvoth involve only tikkun atzmi and are not at all concerned for the pain of the animal. I believe Ramban has this opinion. I hope that both the pain of the animal and tikkun atzmi are what these mitzvot are about. Kindly advise.
Shiluach Haken is clearly and act of compassion for the mother bird, the Talmud tells us however that we do not perform this mitzvah [or any mitzvah] because we appreciate it’e meaning, but rather because that is the will of Hashem. So even when we don’t understand the reason we fulfill the mitzvos wholeheartedly.
The Rambam understands the prohibition of te ox and donkey as the other forbidden mixtures in the Torah, such as wool and linen, and not connected to the animal suffering per say. The Ibn Ezra however explains it is because 2 different animals will suffer from working together, The Sefer Hachinuch explains further, that it causes a sort of emotional pain for an animal to be paired up with a different species and thus the Torah prohibits.
See Sefer Hachinuch, MItzvah 545 and 550.