what i should do is get the inputs in 1 function. from that function you send the skills wich are changed by that input to the server... than the player action checks if a skill is 1 and than handles the movement.
what you do now is handle the movement from the same script as where you get the input, etc...
and also what i should do i put the nosend_frame to on in the player action. and than with proc_local i should run a function wich checks wich animation you must run. and than run that animation

the camera you must keep how it is now.

i guess you have to rewrtie many of your code to work good for multiplayer...