The closest approach is about 600,000 Km away. That's more than twice the distance to the moon. At that distance, to be (just barely) visible to the naked eye, it would have to be about 170km across, which would put it among the largest asteroids in the solar system. In fact, 2024 PT5 is only about 11m across (~36ft). You would need quite a powerful telescope, indeed, to see an object that small at that distance.
The kind that takes more than 2 months to 'complete'. From the perspective of the earth it makes a horseshoe shape. From the 'temporary moon' perspective it gets a trajectory adjustment on its solar orbit.
It's more like a gravity assist that takes 2 months to complete than an orbit.
It's a parabola or hyperbola. Of course, it's not technically an "orbit" since it isn't closed; the Wikipedia pages are called Parabolic trajectory and Hyperbolic trajectory.
An asteroid called 2020 CD3 was bound to Earth for several years before leaving the planet's orbit in 2020
How can something that's in an orbit for years then just leave again?
Is the orbit so big it crosses other planets' sphere of influence?
Or is its apoapsis far enough away for the sun to snatch it away?
Gravitational interactions between Earth, Moon, Sun leading to the orbit never really being stable, probably. The asteroid decided Earth orbit wasn't its' forever home.