No, you do not; any standard user can access and make changes within this directory, especially since it would be completely illogical to require use of the root account to access/modify contents of the directory, yet block servers from being started, etc from within the web ui; alongside that would being permission problems which would then result in what would appear to be a bug being that the content in the directory would belong to root, meaning no other user could access or make use of any of the files. However, I do believe I recall a time in the past where /var/games/minecraft/import did require root to modify; if it does currently still require root access then that would mean that I sometime back went and modified the permissions of that directory to allow anyone/everyone with an account/username to be able to modify the contents of that directory, which can be done as root with the command chmod -R /var/games/minecraft/import 777 and then you can add or modify files as any standard user.
If you are using commandline (SSH, PuTTY, etc) then you may instead use the command sudo -i to gain root access. But for SFTP as @tNt stated requires root logins to be enabled.
Nope, not at all; the server has and stores all of that data. All clients ever do whenever connected to servers or LAN worlds is create, receive, and process packets (aka networking related stuff) along with the visuals; servers handle all the world data, such as TnT exploding, redstone magic, item drops, block breaking/placing, and even more based on the packets that clients send to the server or LAN world. It is also the reason why people tend to lag more in singleplayer worlds than they do on servers (noticeably on low-end or old hardware, or even sometimes modern hardware) so some people actually have created dedicated servers for themselves specifically to play singleplayer in, on a separate machine so that they’d have a smoother experience (not everyone has thought of this method though)
It would be wiser to first delete the existing world folder from within the server directory, followed by dragging in the new world files/folder for a number of reasons, mainly because of the way Minecraft’s world saving works.
No, you’re able to run multiple if you have the resources to do so, it just depends on what you’re doing and/or the server’s configuration. For example, a system running with 1GB of RAM can safely run two servers with 256M each or 340M each, however you may also squeeze in three at 256M if you’re lucky and/or willing to take the risk of causing a system lockup due to lack of remaining resources if/when you do something else, such as building spigot, possibly creating backups or archives, etc. But, you can also test being that your mileage may vary.
That is correct; the reason behind that would be to prevent the removal/deletion of the archive, profiles, and servers folders within the /var/games/minecraft directory, however any subdirectory of the servers directory are/will be owned by whoever/whichever user created the server. You can however copy files out and/or access the files in the remaining directories.