Windows 7 RTM 32Bit vs 64Bit (with 4GB RAM)

The output of isainfo -k shows you in what mode the kernel is running. In your case you are running a 64-bit kernel. Everything inside the kernel is run in 64-bit mode (device drivers, system calls, etc. etc.)

The beauty of Solaris (and plenty other OSs, I assume) is that it can natively execute 32-bit binaries as well. Most programs, tools, utilities that come with the Solaris OS are 32-bit tools. The only exceptions are the ones you can find in /usr/bin/amd64. Those are usually the ones that have to work with kernel structures directly or want to take advantage of the bigger directly addressable memory space. They are chosen automatically (their 32-bit counterparts can be found in /usr/bin/i86) through /usr/lib/isaexec which the tools in question are hard-linked to (/usr/bin/ps, for example, is a hard link to /usr/lib/isaexec).

init only comes in the shape of a 32-bit binary, which is a-okay. It doesn't say anything about what kernel you are running. I am quite sure that the same init from a Solaris 2.3 image will still run perfectly fine under Solaris 11 (under SPARC, that is). It doesn't really do anything exciting.

The short answer is yes, 64-bit operating systems almost always require more RAM than corresponding 32-bit operating systems and 64-bit applications often do require a bit more RAM than corresponding 32-bit applications. There are a number of reasons, but the most basic is that pointers take up twice as much space on a 64-bit operating system as they do on a 32-bit operating system.