Is it one Support slot per complete pair of sections, or do you get a slot for an incomplete pair? In other words, does a platoon with a Command Section, 1st Section and 2nd Section have one or two Support slots available? (Assuming there are no abilities that add additional Support slots.)

You'd just get one support unit if you have 3 sections.

You get 1 support slot per 2 sections, including Command. So:

Command Section and 1st Section - 1 Support Slot

Any 2 of 2nd Section, 3rd Section, or 4th Section - 1 Support Slot

-jay