Home Pin is a pull-the-pin puzzle: each level is a contraption of pins holding back lava, water, treasure or enemies, and the order you remove them decides whether Edward gets the loot or gets buried.
Everything is visible, so it's a pure logic problem — work out what each pin is holding and what will flow where when it goes. Getting it wrong is usually instant and often funny.
Each pin holds back something — lava, water, treasure, enemies — and removing it lets that thing flow. The puzzle is the order, since the same pins in a different sequence produce completely different outcomes.
In most levels yes, which is why the order rather than the selection is the puzzle.
Yes — tap the pins. Nothing to install.