H4 Visa for Kids - Drop box eligibility

[need_visainfo]

I am H1 Visa with an approved I-140. My Visa in the passport is expired, but I have a valid I-797 valid until June 2020.

I am in US and not traveling to India now. My Wife is traveling to India and I scheduled a "H4 Visa" appointment for her, as she is not eligible for drop box. Her Visa interview is on 21st Feb 2019.

Now, my kids will be traveling to India (with my cousin) at a later date in March 2019. One of them is born in June 2004 and is therefore 14 and half years old. The other one is 11 and half years old.

1) Since my wife is attending her Visa interview in Feb 2019, I am planning to schedule a separate appointment just for my 2 boys in March 2019. Are they both eligible for Drop box (Should I answer "Yes" for the question in US Travel Docs, "Do both your parents have valid Visa,")?

2) If yes, what documents should I enclose in the drop box?

3) If they are not eligible for drop box, is my wife allowed to accompany my kids to the Visa interview, in March?

4) I strongly want my wife's Visa appointment to be done in February, so that she need not worry too much for the rest of her stay in India. However, do you suggest rescheduling my wife's appointment to March, so that my wife and kids attend the Visa appointment together?

Thank you and I will look forward for your response.