My car broke down my friend pushed buick with his neon would that cause to throw a rod in engine lateron?

Pushing a Buick with a Neon is extremely unlikely to cause a rod to throw later on. The Neon's engine simply isn't powerful enough to put significant strain on the Buick's engine during pushing. The forces involved would be far too small to damage internal engine components like connecting rods. A thrown rod is usually the result of much more serious issues, like lack of lubrication, extreme overheating, or pre-existing internal damage.