Library.

“An adult Tyrannosaurus rex needed to eat about 700 kilograms of meat per day to avoid starvation.”

The evidence does not support a daily requirement anywhere near 700 kilograms of meat. Peer-reviewed estimates and reputable summaries place an adult T. rex far lower, often around 17-140 kg per day depending on metabolism, with even high-end models still well below 700 kg. The claim appears to confuse a possible one-time binge meal with a continuous daily starvation threshold.

“Eoraptor lunensis is not considered a close relative of Tyrannosaurus rex within theropod dinosaurs.”

The evidence strongly indicates that Eoraptor was not a close relative of Tyrannosaurus rex. Recent phylogenetic work usually places Eoraptor outside Theropoda or at most very near its base, far from the derived tyrannosaur lineage. The only meaningful caveat is that the phrase "within theropod dinosaurs" is somewhat imprecise because Eoraptor may not have been a theropod at all.

“The Tyrannosaurus Rex lived closer in time to modern humans than to the Stegosaurus.”

This claim is true and well-established in paleontology. Stegosaurus lived ~150 million years ago, while T. rex lived ~68–66 million years ago — a gap of ~80–84 million years. T. rex went extinct ~66 million years ago, and modern humans appeared ~300,000 years ago — a gap of ~66 million years. Since 66 million years is less than 80–84 million years, T. rex indeed lived closer in time to us than to Stegosaurus. Multiple authoritative sources, including USGS and the Natural History Museum, confirm this.