Hedgehog

OK, this is not personal legal advice, but merely my opinion as a tax lawyer for your amusement and entertainment purposes only... 
 
1.  If the CO is a tax-exempt entity, a 501©(3) for Federal and similar exemption for state purposes, then the entity does not pay income tax on its charitable, educational, etc. operations.  However, if a tax-exempt entity operates a business that competes with other businesses, the income from that business is considered to be unrelated business income and is taxable (think gift shop or coffee shop at hospital).  For state sales tax purposes, a tax-exempt entity can engage in fundraising activities without charging sales tax.  However, if a tax-exempt entity operates a business (think the Council Scout Shop), they have to charge sales tax on all taxable transactions.  A tax-exempt entity does not have to pay sales or use tax on its purchases that are directly used for the exempt purpose (i.e., it can't buy lumber used to build the Scoutmaster a new deck).
 
2.  If the CO is a taxable entity, it pays tax on its income (which would include donations and popcorn sales) but likely would get a deduction for what it spends on the scouting program presumably because it generates goodwill toward its business (like sponsoring a Little League team).  So as long as the monies raised are spent, there probably isn't a tax issues.  The taxable entity cannot purchase anything as being exempt from sales tax.  The better idea is to set up a tax-exempt foundation to be the CO and to make donations to that foundation.
 
 
 
 
 
 
 

Reach out to the folks at council.  Find the general number off the internet site and call it.  They will help you.
 
Council has the official records and they should be able to give you a printout of what they have.  You should be able to use that print out to get any missing patches.
 
The portion of the blue cards you get after completing the merit badges are not collected and don't need to be reviewed.  The print out from council is all the proof you need.

Similar to others, we don't have adults sign off on T through 1st requiements.  More senior scouts will sign off for the younger scouts.  In our troop, the SM or ASMs only sign off on service hours, scout spirit and SM conference.  
 
At summer camp, our scouts working toward 1st Class get a sheet showing what was reviewed.  The scouts take that to a Guide, APL, PL ASPL or SPL for sign off.