@laurmilangie first part: We derive this whole knowledge about Gods and their incarnation from the written scriptures, and the oldest temples whose walls were/are engraved with stories of these incarnations. Some of these temples' dating goes beyond thousands of years. The oldest scriptures include the Vedas which were orally transmitted since 2nd Millenium BC. We've four Vedas, and one of the first, The Rig Veda was written down around 1500-1200 BC. From here we get to know that Lord Vishnu has 10 avatars (incarnations).
As for good or bad, in Hinduism we believe in the continuous cycle of life and death, and we focus on ethics, values, morals, good deeds, bad deeds. For instance the world, according to Hinduism, is in a stage where gradually the vices will overpower the virtues of the people, and this will result in degradation of soul and morals, ultimately leading to the world's destruction.
As for Shiva, he's the destructive force, yes. But the destructor of evil qualities and the cycle of cosmic creations. Shiva in sanskrit means the auspicious one. He's destroyer in sense that when the evils are rampant, he'd lead us to a path of channeling the virtues and create a new era, by 'destroying' the darkness. There's no creation without destruction :)