In the very first level (ever smile?) my amount of gold does not increase or decrease. Rooms cost nothing to make and the imps will dig gold but can't put it in the treasury. They will walk around the treasury trying to store the gold but all I can hear is the sound effect. They will keep trying to store it until i set them to do another task.

I am also unable to build a hatchery for some reason.

Is this a bug or am I missing something?

Is your treasury full? If so the imps won't be able to store more gold until you either spend some or build more treasury. If this is the case, then it would explain why your gold is at least not increasing.

Rooms don't cost anything to carve out since the imps do this and they are basically your slaves (you can even slap them around to get the job done faster). The cost occurs when you build different room types and they have different prices from what I remember.

You also can only build on claimed land, which the imps also need to do. They do their little dance on the plain dirt and then you'll see it change with a little red symbol on that tile. After that you should be able to build your hatchery on it.

Also I think there was minimum dimensions you need for different rooms. I cannot remember specifics, but a hatchery may need to be at least 3x3 tiles in size.

The first level is pretty scripted in what rooms you can build when. You can mark an area to be dug out by your imps (make sure they can reach the tiles you mark, if you want them to actually dig it out!), then they dig it out and claim it (it goes from a dirt floor to a tile floor with a red tile in the middle, like getlogan said), and then you need to actually pay to put room tiles on the tiles you've claimed. You pay for rooms on a per-tile basis, laying them out one at a time (and being charged for each tile); select the room you want to put down and start clicking in the area you want it to be. To build larger (and more efficient) rooms, you need to place room tiles of the same type next to each other; for most rooms, you'll need at least a 3x3 layout for the room to be effective at all.

After you've built a treasure room, the lair should become available. After you've built a lair, the hatchery should shortly become available. You might need to dig to the portal and let your imps claim that before the hatchery becomes available. I seem to recall always having a fly or two before the hatchery could be built. If it doesn't come after a few minutes, make sure the previous room is at least size 3x3.

They dug it out and claimed the tiles. I build the treasury tiles but they cost nothing to create. The amount of gold stays at 2500. The imps will just walk around and try to store gold in a empty treasure room. They never seem to be able too store it. In a previous save they were still able to. But in that save the hatchery will not become available, even after claiming the portal.

After you placed the treasure room tiles, did it look similar to the image I've attached to my post? If so, I'm not sure what to tell you. I guess you could try uninstalling and then reinstalling the game (possibly downloading it from GoG again before the reinstall, in case the installer is corrupted). If that doesn't work, I'd contact support and ask them about it.

Did you get the option to try and build a lair? You get the lair before you are able to build a hatchery.