The plot is fairly similar along with some changes to make it less like a copy of the original.
The original lines are entirely rewritten to better lines. The graphics and gameplay have improved. As well as the design of the characters and locations.
There was never any intention to remake the sequals of the first game. The likely answer is no.
Yes this game was inserted as a prequal to Tomb Raider Legend and Tomb Raider Underworld. While not clearly referenced in Legend, it was referenced in Underworld greatly. Which there fore makes this part of the "Tomb Raider Avalon Trilogy".
