http://www.irs.gov/pub/irs-trty/chintech.pdf
article 19
Regarding the child tax credit, yes, it means you pay no federal income tax and can still get as much as $1000 free money from Uncle Sam if your income is under certain level and fill 1040 (not 1040NR).
You can always confirm the above mentioned with your local IRS office or call the 800 #, however, sometimes those IRS folks are not very familar with this treaty position, you may need to talk to a few people in their office to get the OK from them. That's what my friend did.