The matrix power plant hack was the exception. In the movie, it’s just a screen of code flying past. If you slow it down, it’s a legit hack.

Trinity checks the software version, to see it hadn’t been updated. She then implements a real hack that that version was vulnerable to. It resets the admin password to a default, letting her log in as admin.

My head canon, at least with Superman, is his powers. He doesn’t have multiple unrelated powers, but only 1 main one. Instinctive momentum control.

• Flying - Momentum control

• Bullet proof - Momentum stopped at the point of contact.

• Heat beams - Changing the momentum of particles he’s focused on.

• Holding a plane by a thin aluminium sheet - Adjusting the momentum of the plane directly.

• No sonic booms, or massive wind - momentum nulling on the nearby air.

In this case, catching a falling person safely makes complete sense. He just nullifies their momentum before they hit.