" Can I add my dependents on the 1040NR and also claim child tax credit for them?"--->Only students & scholars from certain countries can claim exemptions for their dependents (Mexico, Canada, Korea, Japan. and India.) Not as a rule. Only those students and scholars in non-resident tax status who are from one of the countries that can claim dependents (Mexico, Canada, Korea, Japan and India) can claim the Child Care Tax Credit.
Also as you can see,you must file your non-resident tax return Form 1040NR or 1040NR-EZ and 8843. During this period your income is not subject to FICA (Social Security and Medicare) taxes. Normally, on the nonresident tax return, you get your personal exemption and itemized deductions, and you do not get exemption deductions for your spouse and dependents except if you are from Canada, Mexico or South Korea or if allowed by the tax treaty.ONLY students from India may claim the standard deduction on the non-resident forms. For 2010 the standard deduction is $5,700single or married filing separately.
REMEMBER; as F1 visa holder, you are NOT subejct to 183 SPT test for the five years.