No, the Earth will not start to rotate in the opposite direction. Ever.
The reason Earth maintains its direction of rotation is conservation of angular momentum. Just like a moving body resists changes in velocity because it has linear momentum, a rotating body will resist forces that try to change its rotation state. Angular momentum can be moved around in a composite system (consider a figure skater pulling in her arms while spinning), but it doesn't disappear unless there is a lot of friction. Which space lacks.
There is a grain of truth in the confused articles that led to the question: Earth is losing some angular momentum over time. Most of this is due to tidal interactions with the moon. When the moon formed Earth rotated much faster and the moon was close. Mutual gravitation caused tides that made some of the angular momentum transfer from Earth to the moon, slowing the rotation of both (to the extent the Moon now only turns one face towards the Earth, tidal locking) and giving the moon more angular momentum in its orbit, making it move outwards at a very slow rate. There are also tides from the sun (and other planets) but they are too small to matter here.
In reality, the sun will become a red giant in 5 billion years and expand, ending the story of the Earth and moon (ironically in this context, likely by tides dragging in Earth into the sun when it gets close enough to the surface). But if we ignore that, what would happen?
As the Earth's rotation is slowed by lunar tides, eventually it would become tidally locked to the moon in about 50 billion years. The moon would always stay over the same spot, visible only from one hemisphere. But Earth, like the moon today, would also continue to rotate around its axis. It is just that the "day" would be more than a month (about 47 days), corresponding to one full rotation of the Earth-moon system. But the direction would be the same as now, since the moon is moving around the Earth in the same direction as Earth is rotating.
At this point there would still be some loss of angular momentum due to solar tides, so over very long time periods (about 50 billion years more) the Earth and moon would slowly orbit closer and closer. Eventually they would merge into an (again) somewhat fast spinning body (still moving in the same direction!)
In the really long run tidal forces would slow this rotation so the big planet would be tidally locked to the sun. But again, the one-year rotation of the planet would be in the same direction as now.
There is a lot of nonsense claimed on the Internet. Learn the basic laws of physics like conservation of energy and momentum, get used to do rough calculations, and you can usually see through it quickly.