He found it in the ruins of the Gaunt family shack, where Voldemort had hidden it after turning it into a horcrux. Also the curse didn't come from putting the ring on, it came from trying to destroy it with Gryffindor's sword.
The ring which belonged to Tom Riddle's grandfather and the one he converted into a Horcrux. When Dumbledore was hunting for Horcruxes, he went to the Gaunt's house and discovered the ring there. The stone had the sign of Deathly Hallows and he immediately knew what it was.
It was hit by a curse when he put on a cursed ring. He was able to return to Hogwarts and Snape managed to contain the curse, temporarily, in Dumbledore's hand, meaning it looked shrivelled and black. But in the end, the curse was going to spread and give Dumbledore a rather agonising death.
A scalpel, or lancet, or bistoury, is a small and extremely sharp bladed instrument used for surgery, anatomical dissection, podiatry and various arts and crafts (called a hobby knife). Scalpels may be single-use disposable or re-usable. Double-edged scalpels are referred to as "lancets".
While it's no secret that Spider-Man is a genius, he has a tendency to make some incredibly dumb decisions at times, drastically contradicting his scientific mind. In actuality, Peter Parker can easily hold his own in a conversation with both Reed Richards and Tony Stark.