****
This chapter is to clear any confusion.
****
Misa Amane is the same misa from the original series. She made a deal with the shinigami king to let her see Light again.
Yamishi the Mc of this story is basically the incarnation of the original series mc Light Yagami. The two are blood-related and their existence has been merged but not completely. This is why Yamishi can remember an event he wasn't even alive for.
Light Yagami is still in the shinigami realm spending the rest of eternity feeling every death he caused at the same time over and over. He is there to suffer, the one part which is in Yamishi will affect him, but you will see this more in the future.
Anything which happens after the original series does not happen in this version. That means that there were no other kiras apart from those in the in the original 37 episode anime. This also means none of the events of the latest one-shot had occurred.
Ryuzaki or R is not the same person as L. He simply uses Ryuzaki as he knows Yamishi knows of the entire L vs Light Yagami case.
Watari is not the same person as the original Watari.
****
That's about for the info that you might not understand. Also, I hope this clears everything up.
****