Nice discussion!
The article says, "If the Earth stopped spinning, you wouldn't suddenly be launched off into space. Gravity would still keep you firmly on the ground."
Question. What about conservation of angular momentum and any violent reactions here?
The "firmly" part should not imply loose objects wouldn't go flying at the instant the Earth stopped rotating, just as things go flying in a car wreck. The speed they would instanly have would be about 1100 mph * cos( your lattiude). But, this speed isn't fast enough to become untethered to the Earth.
The energy necessary to actually stop the Earth must eqaul or exceed that angular momentum energy. This energy, however, might be used to alter spacetime to cause a gentle stop, even if very quick. From GR we know that how things (masses) move is tied directly to the shape of spacetime. Suddenly alter spacetime and things move suddenly differently.
Frame-dragging is the term used that describes how a rotating body drags spacetime with it. [ It was first measured, IIRC, by Gravity Probe B. ] What if you could, with your magic wand, dramatically force spacetime to be dragged in the opposite direction? The new "path of motion" would suddenly be altered and things, firm or loose, would not experience any flinging... maybe?
It would take, however, someone very knowledgeable about GR to answer this question, but I think it is a fair question.
Question. Is this true? Consider the geocentric Earth or heliocentric Earth model.
Adding to what
Wolf stated, the non-rotation is meant to be relative to the fixed stars, not the Sun. Just like there is no seasonal change, or much of one, with Polaris. There would be only half a year where the night sky would be visible, and the Sun would fill the other half.
George Darwin was the first to explain tides. He offered his hypothesis of the Moon moving away from the Earth due to the tidal effects. His 2 hour rotation rate was based on a speed that would allow material from Earth to spin off the Earth, which was his idea about how the Moon may have formed.
The modern figure is abut 5 hours per day. This is by reversing the clock and having the Moon move close enough to the Roche limit.
The impact that formed the Moon would have greatly altered the Earth's rotation speed, so any guess as to its orginal speed may be wild. Perhaps exoplanet rotation rates, once determined, may help give us a better idea.