I've noticed that when your of server or not by your furnace nothing cooks. The same thing with plants but they don't grow. Wouldn't you think that in 5 hours of being off server your 64 clay would of hardened or your wheat plant would of grow and would be ready to harvest. Also in your single player games too. I mean I wouldn't expect that my game would go without me on single player, but when you leave your house everything stops cooking not so much plants not growing in single player though. If you know why this happens PLEASE comment below and tell me.
Well, it's really quite simple. In order for that to happen, the chunk has to be loaded. If the game were to keep EVERYONE's chunk loaded, wherever they are, it would lag the server to the point of being unplayable. Think of all of ECC loaded at the same time. That hardly happens as is, but if the server loaded everyone's chunks all the time, even when they were offline, that would probably happen. It would then likely, like I said, lag the server to the point of being unplayable. Now, if another player is IN your chunk (this is the bonus of living in big towns), then your plants will grow, things will smelt, etc.. But otherwise, no.
Oh, didn't look at your post completely. As for the online part, you just need to stay within the zone of your house where it loads your house. Basically, stay within sight of your house, and things will cook and grow because the chunk is loaded.