Do you get those powers that Harkon was using like when the red field went around him, Are there bonus powers or something?

no bonus powers other than the 2 rings and 2 amulets from doing radiant quests, and maxing the perk tree

What do the rings and necklaces do

amulet 1: lets you summon 2 gargoyles
amulet 2: surrounds you in bats that do extra damage to close enemies
ring 1: increases health by 100 and extra claw damage
ring 2: increases magic by 100 and extra regen? idk.