Are Hezbollah's part of the regular Lebanese Armed Forces (LAF) ? If not who funds them ?

no, they are a paramilitary revolutionary group who for years have tried to re-islamize a christian arab country. In 2006 they overtook half of the city of beirut and declared martial law, with their head, Han nasrallah delcaring an unofficial and unrecognized coup. They are funded, armed, and supported directly by the Iranian Revolutionary Guard/government.