What is the process for manufacturing hand-sanitizing antibacterial
gel such as the one produced by Purell, Dial, Kimberly Clark, etc?
Which companies manufacture the machinery used in this production
process? What would be the estimated Economic Order Quantity (EOQ) for a
typical batch in a small production line for this type of
product(including packaging)?

Have you considered buying in bulk?  It is seldom economic to compete
for bulk production of such materials.

Have a look at:

   www.chromate.com for a start.

Anduril-ga