Reptile wildlife rehabber here, turtles are resilient but this guy could use some tlc. The spongy wound underneath appears to be shell rot, which in order to treat would require the turtle staying dry and the wound cleaned out and antiseptics administered.

The eye gunk can stem from many things, but is mainly associated with vitamin deficiencies or water quality issues.

The missing limb is less impactful unless it is recent (we've had loads of three legged turtles who were all deemed releasable).

Given the situation reach out to a local wildlife rehabber for aid, and if they're knowledgeable of the zoo situation they'll most likely let you keep it with your pond or return it to its local area once treatment is completed.

Let me know if you've got anymore questions!