Technically yes. They could be the cause of the spike or potentially if something else is stealing all of my computers resources it might take a long time for the local script to be scheduled again. Remember that software takes turns running on the CPU so the script might not technically run for a while depending on the state of my system.
I believe so. Usually this is handled by multiplying the speed times the time between frames. That will effectively teleport you. However it might not handle all inputs in that time depending on how Roblox handles it. And note that some systems will cap the maximum delta time specifically to stop large teleports (I believe the camera does this)
Generally it’s a tween. Usually positions for items aren’t updated all the time and get tweened between several control points anyways.
Unless told not to, Roblox servers intrinsically trust clients and will always accept the position a client sent. So the client tells the server where they are and the server blindly tells everyone else. These messages are probably tweened, but I can’t say for sure.
Yes. If my computer has too many things fighting for CPU time I can end up completely stalling Roblox.
No. A stall would basically make stuff late. Trying to compensate would actually likely make the problem worse so systems usually drop it if they can.