www.logiccircuit.org

I mean can I expand the white area where I can draw

No you can't. But you can make your circuits smaller by breaking it up to sub circuits and use them. You can also group wires with splitters. Having smaller circuits makes it easier to understand the design, avoid and find errors.

I also wanted to do that. I'm working on project with a goal quite opposite of "easier to understand the design, avoid and find errors". I wanted to show the complexity of circuits, and tried to do (at least for the first step) an 8-bit ALU with only NAND gates (and tri-state), all in one circuit.
Is there any way to expand the workspace outside of the program's bounds? I mean changing the source?
Is there any performance drawbacks of having one huge circuit instead of smaller ones connected?

No, you can't do that without changing the source.
The execution performance will not suffer from such expansion, but the visual might. It depends on how many element you will have.
BTW, you can make you circuit bigger than the drawing boundaries now just move elements beyond the white space.
Also you can show complexity in different way. For example you can open project report. It will show how many various elements you have.