Is buying state-owned equipment designated for auction, which its custodian sold without the officials' knowledge for a pittance, considered unlawful (haram), and what is its expiation if it is?

The guard's sale of another's property without permission is void. Your purchase from him, knowing that he does not own it or have permission to sell it, is unlawful (haram) and an act of assisting in something unlawful. The expiation for this is to repent to Allah, return the equipment to the institution, and seek the price back from the guard.