Hi, a little late with the info.
The biggest store where people get quilting cottons in Singapore is a store called Spotlight. It is a chain craft store from Australia, somewhat like Michaels. There are also a couple of smaller (kind of like LQS) in Tanglin area.
Don't worry about cars. Public transport is everywhere. Cabs are relatively cheap.
If you are shipping stuff (packages) from US, many people use vpost. Your friend might want to check that out.