4 Answers

Looks like they were always round.

The first formal rules were devised in 1892. Initially, players dribbled a soccer ball up and down a court of unspecified dimensions. Points were earned by landing the ball in a peach basket. Iron hoops and a hammock-style basket were introduced in 1893. Another decade passed, however, before the innovation of open-ended nets put an end to the practice of manually retrieving the ball from the basket each time a goal was scored.

Yes, flat when deflated.

They had a square one, it did not roll off shelves when stored, but was difficult to dribble, and bounce straight!  The guy who invented the triangular golf ball invented this! 

Nowadays, it only occurs when they get run over by a car.