The installer needs to find the game in your Windows Registry. If you are using a "repack," the official patcher might not see the game. Pro-Tip: Should you go higher?
If you just want a stable game, and go straight to 1.0006 . Better yet, look into the "OGSR Engine" or "ZRP" (Zone Reclamation Project) . These aren't just patches; they are community-driven updates that fix thousands of bugs that GSC Game World never got around to fixing.
Moving from 1.0000 to 1.0001 usually preserves saves, but moving backwards from a higher version will definitely break them.
While version 1.0001 was the very first update released shortly after the game's launch in 2007, it is rarely used today. Most players aim for (for specific old mods) or 1.0006 (the final official stable version). 1. Why version 1.0001?