Cross-installing programs to share them between Windows and Ubuntu

You are not going to be able to install programs in the third partition so they can run on both OSes. There is a reason why you need to have different downloads depending on your OS, each OS has many different requirements for software.

You should be able to set it us so that licenses are shared, if you need them, and you may be able to set it up so that files that are produced are shared automatically, and maybe even IDE setting but the programs themselves will have to be installed in each system.

One workaround might be to set up x11 forwarding from one OS to the other but that would require you to have both OSes running at the same time which would be quite janky.

As a side note if you had 2 partitions with Ubuntu instead of Ubuntu and Windows this probably would be possible.

For almost all programs, no. This is due to Windows and Linux having different API (Application Programming Interface) calls and system calls. API's are functions and define how programs communicate with one another. Typically, they are included in libraries or may be part of the operating system. System calls define how programs request hardware support/activity from the kernel. It is possible to translate API calls and system calls of one operating system into another, but it requires a tremendous amount of effort. WINE is actually a prime example of translating Windows APIs into POSIX (e.g. Linux) ones. This creates a compatibility layer between Windows and Linux, allowing some Windows software to run on Linux. Additionally, Windows and Linux have different binary executable formats. Windows has the Portable Executable (PE) format and Linux has the ELF (Executable Linkable Format).

All of that said, I don't think what you're trying to achieve is possible without significant effort. Maybe (big maybe) you could install WINE and configure it on your shared partition so that it could hold programs for both Windows and Linux. But that's a wild theory. What fellow user Jeff said regarding licenses and other files is more likely to be possible and much easier to accomplish.