Sure it is infallible, and that is the scary part of Catholic religion. In theory, the Pope could repeal the law of gravity and invoke the doctrine of infallibility. Then anybody who disagrees with the Pope, anybody who says that law of gravity is still around, is not a good Catholic, by definition.
Absolutely Not. First of all the Pope never invokes anything in isolation. He builds a consensus within the Magisterium (the college of cardinals, bishops and the curia). In order to become 'infallible' it must be proclaimed 'ex cathedra' from the chair, and then ONLY in matters of faith and morals.
The Pontiff cannot revoke the Law of Gravity. His encyclicals, while authorative, are not considered infallible and therefor beyond error and question. As far as i am aware, the last time infallibility was invoked, was by Pius XII, in 1950, in promulgating the doctrine of the Assumption of Mary. It is very rarely used, and when it is used, it is usually to settle abstruse theological debates within the Church.