How capturing works
Only Infantry and Bazookas capture. A building has 20 capture points; each capture takes off as many points as the unit's health (a full unit takes 10, so two turns). If the unit leaves or is destroyed, the building heals back to 20.
Repairs and supply
A unit starting your turn on one of your buildings is refilled and repaired by 2 HP, paying 10% of its cost per HP. Ground units repair on cities, factories, HQs and labs; air units on airports; ships on ports.
Spend it all
Unspent funds do nothing. Early on, build Infantry to grab neutral cities fast; every city you take adds income every day for the rest of the game.