MOULa as the official shard is protected against cheats like flymode or usage of /jump command.
MOULa which is runs by Cyan, you must follow their advices. Cyan authorizes 2 type of clients on their shard (which is quite unusual since almost any other fan-base shard have more restrictive rules): running on the standard external client OR running on an internal client.
To sum up: MOULa, as of today, has 2 standard external clients: the normal 1.912 and the skydiving 1.906. The 2nd one cannot be distributed anymore unfortunately. We must wait for the next update. For those having it, usage of it is perfectly fine
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The internal clients must be compiled by you or you can also take what I'm calling the standard internal client also known as plClient which you will see referred on this forum as well as on MOULa's forum as The CWE client. Adam Johnson aka Tsar Hoikas on this forum provided this week the newest release of it.
You have to find how to enable the flymode by yourself. And quite frankly...MOULa has not that much out-of-reach extended areas (except maybe Er'cana). If you read at what Adam wrote, you have to follow his advice: the internal client can be really harmful so you must know how to use it properly and in ages specifically created to let you do that. Using it in your own ages (NOT the public ages, never) it is at your own risk. If you have many avatars, preferably make 1 for using internal client. If you do break something, you will save your main avatar. My Annabelle on MOULa she is rarely on plClient, I might use it for things I know it won't break anything. I'm using my own specific avatars for plClient usually.
As for "MOULa offline", there's no MOULa offline possible. MOULa has always been based on a server perspective. But what is a server privately owned with a sole & unique user?
A MOULa "offline" if you want
For this, you have to be savvy on how to build yourself a server and run it. You will need the internal client, plClient, to access it. Even privately owned, you must be conform with the Open-Source rules edicted by Cyan. I don't know them much since I'm not savvy enough to run myself a server but I know at least one: you cannot modify the assets of MOULa (scene objects, python modifiers, sound regions, etc.) The code can be modified and improved though. You can participate in the general improving process started by H'uru or OpenUru.org teams, see respective repositories for that.
I hope it clears up some of your questions. Maybe some others will be able to add some specific things I forgot to mention.