The balance wheel gets a small energy push through the escapement on each tick. The barrel's mainspring has enough force to just kickstart a stopped balance wheel. The balance wheel doesn't really need much "winding" - it's equivalent to the pendulum of a grandfather clock.
It's really fascinating seeing this mechanism alive, even in a simple mechanical kitchen timer with plastic gears. When wound up, the balance wheel starts to swing a little and quickly accelerates on each tick.
Same question. The balance wheel/hairspring has to be losing energy overtime to friction (however miniscule). Otherwise we have ourselves a perpetual motion machine
To add to the other answer, that friction (and the intertia of the balance wheel) is actually factored in when regulating the watch. The pallet fork gives the balance wheel a nudge on every "Tick" then the pallet fork stays stuck until the balance wheel swings around and back and jolts it in the other direction (the tock). Basically a little bit of energy is released from the mainspring via the escapement to the pallet fork to the balance wheel on each tick/tock.
