The same way you save in survival. Click the esc button, and then save and back to title screen.
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In Minecraft Classic, mobs can't spawn, so they can't exist naturally. If you play the Survival Test, and when mobs spawn there, you can save it and open it in creative mode so then the mobs can stay there. However, in Minecraft Creative Mode, mobs can spawn, but they can't hurt you because you have no healthbar.
Minecraft saves automatically every 5 seconds, or when you pause the game
You pause the game by pressing start, then proceed to press R1, L1, R2, and L2 at the same time. This should prompt a screen to show up, which will help you activate creative mode in the game. Now that creative mode is on you should have unlimited money, and Spoot the Llama, who tells jokes. Spoot can be found in the miscellaneous section of the decor section, he's not the first option, btw. On the down side, you can unlock no challenges while creative mode is on, and you cannot turn it off once on. Which makes it a good idea to save your game while activating creation mode, there'll be a screen for it.
I'm afraid not. You have to buy the full game in order to use the save feature.
Yes, Minecraft can either be played single player on a local save, or multi player on an online server.