As soon as I start a new game, and I build a house, a fire instantly burns it. The date is also flying by 1 month per second. I'm getting warnings and messages constantly. This is ridiculous!!!

What speed do you have the game set at?

The GOG.com version has the in-game and mouse speeds set to 100% by default: why they set this is beyond me. You can lower this by going to Options -> Speed Settings and lowering each. I recommend 80% for the game speed and 70% for mouse speed.

The tricky thing about game speed is as follow: while every speed up to 90% (included) still runs like it was intended with the original game, at 100% it will use all the CPU cycles it can. With our modern CPU, it means the game will just go totally crazy.

It goes the same way for Caesar 3 and Zeus.

That's mostly true. You can solve the cycle issue though simply by using of the widescreen patches so that the game is forced to draw the screen to your native screen resolution, which makes the 100% speed go at a more appropriate speed. I noticed that, at 1024x768 and 100% speed, it was too fast and unplayable.