According to a caption in MARVEL TEAM-UP #27, Peter was a physics major during his undergraduate studies.
A caption in the following issue stated that he was pursuing a bachelor's degree in physics.
In AMAZING SPIDER-MAN #243, he received a letter from Empire State University informing him that he'd been approved for second-year studies in the graduate ...
In the Ultimate Marvel universe/line of comics, the original (Natasha Romanova) Black Widow dies, and a couple of other characters take up the name while working for SHIELD.
One of the other characters who takes the name Black Widow is the Ultimate version of Spider-Woman, a female clone of Peter Parker who most definitely has spider powers.
Black Widow, along with half of Manhattan, receives viral spider powers in the animated series Marvel's Spider Man - Spider Island Part 2.
We don't see her use spidey-sense, but she slings web, crawls on walls, leaps high into the air and punches like a champion,
As far as I'm aware Black Widow has never had physical Spider-Man-like powers. However, in Amazing Spider-Man Vol. 1 Issue 86 Black Widow upgrades her costume and equipment. As part of that process she upgrades her Widow's Line: an imitation of Spider-Man's web shooters.
Click image to enlarge.
Her suits have also been shown to be able to cling to walls ...