Ineed with art how were greek gods and godesses portrayed in greek sculpture? how were they portrayed this way? what periods of the sculpture do they appear?

I can answer the 1 question The reason many Greek Gods and Goddesses were depicted in sculpture was because the people who created, surrounded or viewed it wanted to be protected by the certain God or Goddess. 
So, of course, they were always portrayed in their strongest form, they were armed with either a weapon or an implement that aided them in doing their "job". It's not that hard to work this out when you see the sculptures, have a look around at some images, and draw your own conclusions as well. That's the best way to do it

Cthe lindisfarne gospels

These traits are all equally important in recognizing the validity of artwork mainly due to an artists' consistent style and reputation which they have developed over a lengthy period of time. most famous paintings contain specific characteristics of the artist who created it. an appraiser would pay close attention to certain key elements within the painting, as well as an accuracy in measurement and color shade. blended textures and outlines are essential in recognizing an authentic piece from a copy. signature and imagery exist in epic proportions to balance out each trait as they coexist in harmony, depending on preference and style of each artist. no two original pieces are virtually identical, although it may be almost impossible to see discrepancy with the naked eye.