Is the money obtained from selling parts at a higher price than what I paid for them permissible (halal), especially since the buyer does not know that I am profiting from this, and they do not pay me for my effort? And is the money I earn from reducing the prices of parts I purchase for the institution I work for permissible (halal)?

In both cases, the questioner is an agent for purchase. An agent must act in the best interest of their principal. It is not permissible for the agent to take anything for themselves without the principal's knowledge and permission. If the principal is aware of the true situation, and that you will profit this amount from them, then there is no harm in it for you. Otherwise, it is not permissible for you to take an amount greater than the actual price at which you purchased the item.