noglider 

I wouldn't say you shouldn't have bought from China on ebay. A larger fraction of those transactions prove to be bad, but you have to build that into your risk model. Most of these people are honest but problems happen. I think the important thing here is the time it takes to get your daughter rolling. Try to make it work. You can use the 10-speed chain. What chainrings and cog sizes do you have? Better to have gears that are too low than too high. And how long are the cranks? They might be short, and that's a good thing, too.