What is the CPSIA?

Here is a collection of links where you can see a wide variety of tracking label solutions.

Yes, any maker (small or large) of cloth diapers must comply with CPSIA. The required testing under the law, however, will depend both on the type of diapers you make as well as the CPSC’s final definition of a “child care article.”
Natural or synthetic textiles are now exempt from lead testing, therefore the parts of [...]

Yarn, both natural and synthetic, is on the CPSC’s list of materials exempt from both third party lead testing and phthalate testing.  So any knitted or crocheted product that is made entirely of yarn does not require any third party testing.
However, if you add a button, zipper, or any other part not made of yarn, [...]

Yes, with a couple of caveats.

Here is a list of materials that you do not have to send to a laboratory in order to prove that they are lead-free.

What information has to be put on the label or alternatively, somewhere on the product and/or its packaging?

the name of the manufacturer or private labeler
the location of production (city, state/province, and country)
the date of production OR a mark, such as a batch number or cohort number, that you can use to look up the date [...]