How the player characters actually move without remotes?
is it possible to apply it into a part that player controls without remotes and show movement in serverside?
I think this is done through client physics ownership. Basically if some sort of force/physics is applied to the character on the client side, it automatically replicates to the server side. That’s done on purpose by Roblox to reduce server stress and movement lag(because I think the physics are calculated on the client instead of the server). The negative aspect of this is that it allows exploiters to apply their own fake physics to the character and do things such as increase its speed, make it fly, etc.
There have been attempts of creating server-sided characters/humanoids by the community, such as the chickynoid. Although the cost of this is that there may be delays if the client’s ping is high.
You can change the physics ownership of a part by running BasePart:SetNetworkOwner(player) if you pass in nil instead of a player the network ownership is given to the server(just like any normal non-character part).