Getting ITIN for nonresident alien

1. Since your wife never lived in USA in 2016 and she did not have an ITIN number I don't think you can file jointly, but I am not one hundred percent. Try to answer the questions asked by turbo tax, I remember turbotax asks if you are married and if you and your wife lived in US. Just answer them and let Turbotax decide how to file if possible.

2. I think you will get child tax credit since you are supporting your child financially even though they are in India. 

3. I took my wife to the Social Security office in 2001 (at that time I was on H1B visa and she just entered US on H4 visa). She applied for her ITIN card at the social security office. It took us a few weeks to get the card delivered to us by mail.

You can get an ITIN number for your spouse but you have to apply thru the mail with your tax return. If you kids are still in India you cannot get the child tax credit. The kids must be residents of the United States and have been in the country for more than 6 month for the filing year. You would need to submit US medical records or school records along with passports showing date of entry. See Pub 1915 and the W-7 instructions

You can file jointly with your spouse. You cannot claim your dependents (children) on your tax return until they actually live in the states.
They have to be here more than 180 days and be here as a resident.. You also not be able to claim the child tax credit for them on prior years.

You can always get an ITIN number for a spouse no matter where they live. You can NEVER get an ITIN number or the child tax credit for dependents that live out of the country.