I hope you aren't paying for all these apps. The reason you can't install "any" app is that so far, you haven't been selective about what you try to install. I'm sure you know that iMovie and GarageBand do not run in Windows at all. For your computer, you have to choose apps that run in the OS version you have, and on the PPC architecture. Any app with a requirement that includes OS 10.3 (or as far back as System 7.1) is for PPC architecture. Others that require a minimum of OS 10.5.8 could be for PPC as well, but we need the developer to tell us. Most of them are this thoughtful.
definition:
-- architecture (computer) = main board design related to processor type, ROM chip, firmware, expansion slots, etc. that determines how a computer works.
Your computer is Mac G5 architecture (PCI-e or PCI-X depending on build date) most specifically. It is Mac PowerPC more generally. The PowerPC processors ("PPC" for short) include such types as 601, 602, 603, 603e, 604, 604e, G3, G4, and G5. Here are some ways that applications are designed relative to architecture and OS version:
(1) -- Java (can be designed to install on almost any architecture and corresponding OSes, such as Linux, OS X, Windows, or may be limited to recent architecture designs and recent versions of OSes).
(2) -- X86 (for the style of architecture many people call "IBM-PC" or just "PC". These are recognized by the file naming style "filename.exe")
(3) -- Mac 88K (for Mac architecture with pre-PowerPC processors, such as the Motorola MC68040.
(3) -- Mac classic (for Mac PowerPC architecture and OS 9.2.2 or earlier -- some apps may run on OS 7.1 to 9.2.2, others may be limited to OS 9 - 9.2.2)
Styles (4) to (8) are recognized by having the file naming style "filename.mpkg" or "filename.pkg" for the installer package. The resulting app is recognized by the naming style "filename.app".
(4) -- Mac OS X PPC only (can run on a PPC Mac if other requirements are met, such as minnimum OS version)
(5) -- Mac OS X universal binary (can run on both PowerPC and Intel Macs)
(6) -- Mac OS 10.5 ["Leopard"] universal binary (can run on both PowerPC and Intel Macs, but must be OS 10.5 or later)
(7) -- Mac Intel (can run on Intel processor Macs only; may have additional requirements, such as OS version)
(8) -- Mac OS 10.6 ["Snow Leopard"] (for OS 10.6 or later only -- also happens to be limited to Intel, since OS 10.6 can only be installed on Intel Macs)
A very few big bucks apps such as Photoshop v.7 were available as a combined Classic - OS X app.
When using a PowerPC Mac, any app ("filename.app") that is for Intel-only will appear with a prohibitory sign over the icon. That means the circle with slash, like a no U-turn sign in Europe.
In a few rare instances, one could possibly use an app on a lower OS version or older architecture (but still Mac) than the app is offered as, but the developer added a check process to the installer or to the app iteslf that limits it. For those, one could hack it to make it install or launch on an older system design, but with possible poor performance or bugs.
An app called Winebottler can wrap a Windows app in an OS X package with DLL files and a substitute for the Windows kernel file, thus permitting the app to launch and run in OS X Intel-only.