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He has a current wife needing an ITIN.
He has an ex-wife who is the mother of his 2 1/2 year old child who was born abroad and has no CRBA.

Read the details on multiple pages here https://eg.usembassy.gov/u-s-citizen-services/child-family-matters/birth/
there are ways listed for only one parent to attend the interview. You will need written consent from the other parent. 
 
For tax purposes, what will you gain by having a citizen child with no SSN and has not lived with you more than half the year?  We don’t have dependent children so I am not that knowledgeable on dependents is why I ask what it will do for your tax return?

She's finishing up her professional degree. I have started her CR1 for her. 
Thank you 

Do you have the actual passport with you in the US, not a photocopy?  If so, you mail everything  to Austin, TX for processing. Included should be:
the joint tax return (signed by both) a statement electing for her to be treated as a resident alien for tax purposes (signed by both) W7 application for ITIN (signed by her) Her actual passport for identification The address and other information are on this IRS web page  https://www.irs.gov/individuals/how-do-i-apply-for-an-itin
Option 1 on that page is your only choice if she is not in the US to go in person for Option 2 and 3.
 
if you are abroad with your wife, you have to find an acceptance agent who can certify her passport. She must be present.

You have the option of using one of these 5 documents to prove US citizenship. 

Yes. In regards to the I-130A spouse supplement there is a section to upload that PDF.
After the "Review" page it'll take you to the payment portal at pay.gov: https://www.uscis.gov/forms/filing-fees
If You File Online If you file your form online, the system will guide you through the process of paying your fees with a credit, debit, or pre-paid card. Bank account withdrawals are also available when paying online. Once you are ready to submit your form, the system will automatically direct you to the secure Department of Treasury site, pay.gov, to pay your fees online.
 
We only use pay.gov to process fees. Always check the website address before you pay. Beware of scam websites and scammers who may pretend to be a USCIS website.

You can explain in the "Additional Information" section that you misplaced it. I recommend filing the petition online: https://www.uscis.gov/i-130
 
Also, when you find it make scans/copies for your records.