I'm only starting to dive into this project, with only some basic knowledge.

In the very first day, the VC compiler is enabled using the vcvarsall.bat x64 library.
I'm currently on x86 Windows, and I want to know if I will be able to compile all the future code in x86 using the x86 compiler library just fine, considering that the project itself is created for x86, or do I need to actually get the x64 Windows?

You can compiler latest code as 32-bit, except few signed/unsigned and casting uint64 to size_t warnings which are trivial to fix. But the bigger problem is runtime. Currently Casey is requesting a ton of memory - >5GB. That won't work for 32-bit application. So you'll need to reduce memory he's requesting from OS to make it work. It's not a big deal, you can easily do that.

Thanks. I guess by the time I get to the memory heavy part I might transfer the project to another machine anyway.