(1) yes each char is bound to a server - however you can UPLOAD your character to another server thus retaining what stats and levels he has achieved on the previous server.

(2) if your server allows downloads it is possible however it is not guaranteed to be safe transferring between servers - there have been instances of totally lost characters (glitched)

(3) yes as long as the client software remains running but this entrails leaving your computer on and steam/ark running to maintain that client server (dedicated) this may result in a heavy load unless the server/client/pc is restarted after a set period

(4) it is easier to start new characters on other servers and maintain your other characters elsewhere - by having multiple characters you can explore different stat/configurations and is sometimes preferable to transferring between servers.

To summarize it is actually easier sometimes, to create new characters on different servers, especially hosted as dedicated, if the dedicated server is not available you can still play on another server. Personally I run multiple characters as it is much easier than transferring and all the effort to do so.